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This paper investigates the analytical fuzzy findings of a two-dimensional fuzzy fractional-ordered heat problem including some source of terms under certain conditions. The Sumudu residual power series scheme (SRPSS) is an innovative novel to deal with the combine form of the Sumudu transform (ST) and the residual power series scheme (RPSS) which efficiently generate analytical results in rapidly converging series forms. The Caputo derivative is applied to model the physical problem. The most notable aspect of this algorithm is its ability to generate results quickly and without difficulty as compared to the conventional RPSS. We present three numerical cases of 2D heat problem with fuzzy fractional order to express the performance and validity of suggested scheme. Graphical analysis from the derived solutions reveals that SRPSS is straightforward, accurate, and suitable to analyze the findings of fuzzy fractional problems.

In this paper, we propose competitive predator-prey models with a small immigration into the prey. The dynamics of these models are investigated by addressing the boundedness, coexistence, and extinction conditions, as well as the local and global stability of equilibria. Immigrants stabilize the systems and increase the probability of coexistence. A Hopf bifurcation analysis shows that the model with Holling type II exhibits a Hopf bifurcation with respect to immigration parameter, but there is no bifurcation of the model with Holling type I. The numerical results support the theoretical results. Additionally, incorporating a few immigrants into the prey has a high sensitivity when the dynamic is periodic, but it has a lower sensitivity when the dynamic is stable. The obtained results can be biologically interpreted to improve the survival of species in the environment by adding immigrants. The rescue effect is considered as one of the implications in the real world that interpret the obtained results in this study.

Abstract Reformulating the physical processes associated with the evolution of different ailments in accordance with globally shared objectives is crucial for deeper comprehension. This study aims to investigate the mechanism by which the HB virus induces harmful inflammation of the liver, with a focus on early detection and therapy using corticosteroids or chemotherapy. Based on the developed hypothesis, a new mathematical model has been created for this purpose. The recently developed system for HBV is $$SEI_{1} I_{2}R$$ S E I 1 I 2 R , which is examined both quantitatively and qualitatively to determine its actual effect on stability. Reliable conclusions are ensured by examining the system’s boundedness, positivity, existence, uniqueness, and conducting local and global stability analysis-all crucial components of epidemic models. Global stability is tested using Lyapunov first derivative functions to assess the overall impact of asymptomatic persons and chemotherapy treatment. Additionally, the Lipschitz condition is used to confirm the unique solutions for the newly built HBV model using methods from fixed point theory, thus meeting the requirements for uniqueness and existence. Since the population must maintain this property, positivity is confirmed using global derivatives and Lipschitz criteria to calculate the rate of change in each sub-compartment. Applying the Mittag-Leffler kernel with a fractal-fractional operator to continuously monitor the HBV virus for liver cirrhosis infection yields dependable results. Furthermore, the current situation regarding the HBV outbreak pertaining to liver cirrhosis infection, along with the control measures implemented following early diagnosis through asymptomatic measures and chemotherapy treatment under constant observation, are established to prevent chronic stage infections. Simulations have been used to study the true behavior and impact of HBV in asymptomatic persons receiving chemotherapy for liver cirrhosis infection in the community. This research is essential for understanding the spread of viruses and developing control strategies based on our validated findings to mitigate the risk factors associated with liver cirrhosis.

This study examines the modified Sardar sub-equation method (MSSEM) for deriving the novel solutions of the (3+1)-dimensional p-type model. This framework is commonly employed to explain the behavior of optical solitons in nonlinear media. The applications of MSSEM allows us to acquire the precise analytical solutions, which incorporate a diverse array of optical soliton solutions. We discuss the dynamical structure of the solitons, bifurcation and chaos theory to develop the multiple soliton solutions, including rational, hyperbolic, exponential, and trigonometric functions and depending on the principle of balancing equation. Moreover, by using bifurcation and chaos theory, we examine the governing model with and without the perturbation term and provide the three-dimensional, two-dimensional, and density profiles to improve the clarity of obtained results. The different aspects of the solutions are evident in our visual representations. These solutions are applicable to a wide range of domains, including fluid physics, oceanography, physics, engineering, and nonlinear optics.

Abstract In this work, we solve a system of fractional differential equations utilizing a Mittag-Leffler type kernel through a fractal fractional operator with two fractal and fractional orders. A six-chamber model with a single source of chlamydia is studied using the concept of fractal fractional derivatives with nonsingular and nonlocal fading memory. The fractal fractional model of the Chlamydia system can be solved by using the characteristics of a non-decreasing and compact mapping. A suggested model with the Lipschitz criteria and linear growth is studied both qualitatively and quantitatively, taking into account boundedness, uniqueness, and positive solutions at equilibrium points with Leray-Schauder results under time scale concepts. We examined the framework of local and global stability and insight into Lyapunov function properties for the infectious disease model. Chaos Control will employ the regulate for linear responses approach to stabilize the system following its equilibrium points. This will take into consideration a fractional order framework with a managed design, where solutions are bounded in the feasible domain and have a greater impact at the lower minimum infectious rate. To illustrate the implications of fractional and fractal dimensions with varying interest rate values through simulations with Newton’s polynomial method under the Mittag-Lefller kernel. Additionally, a comparative analysis of results is also derived by employing power and exponential decay kernels at various fractional orders.

ish skin leather is a sustainable alternative to traditional leather production. The goal of this study is to create a recipe for turning raw stingray leather into protective gloves for hands. The process flow of Stingray Leather Processing and optimization of each single step has been done. The technique is based on tanning agents, formulating new processing methods, conducting an extensive market analysis, and examining the environmental impact. The processed stingray leather was evaluated for resistance to abrasion, cur, and puncture resistance, and it was found that the stingray skin gloves showed better cut and abrasion resistance than the conventional gloves available in the market.

Objective: The Sentinel Node vs. Observation After Axillary Ultra-Sound (SOUND) trial reported that omission of axillary surgery was not inferior to sentinel lymph node biopsy (SLNB) in those with cT1 breast cancer and negative preoperative axillary ultrasound. The aim of our study was to evaluate the clinical characteristics of early breast cancer patients undergoing breast conserving surgery (BCS) at our institution in order to investigate the exportability of SOUND criteria to our patient population. Materials and Methods: We retrospectively reviewed patients with cT1N0 breast cancer undergoing BCS and adjuvant radiotherapy according to the SOUND trial criteria. Comparison was made between the eligible group of our cohort and the SLNB arm of the SOUND trial. Results: The proportion of younger patients was higher in our eligible cohort (37.7% vs. 17.5%, p = 0.002). Postmenopausal patients were more prevalent in the SOUND trial (79.4% vs. 56.6%, p = 0.004). On final pathology, tumours were more likely to be upgraded to T2 in our group (26.4% vs. 4.4%, p = 0.001). Patients in our cohort were more likely to receive adjuvant chemotherapy (37.7% vs. 20.1%, p = 0.002). Conclusion: The clinicopathological differences between our cohort and the SOUND trial population could be attributed to aggressive tumours in Bahrain compared to Western countries. Our study may influence others to investigate the applicability of the SOUND trial in clinical practice. Nevertheless, it is a study that should generate multidisciplinary discussion in the de-escalation of axillary surgery.

This study aims to investigate the properties of fractional calculus theory (FCT) in the complex domain. We focus on the relationship between the theories of special functions (SFT) and FCT, which have seen recent advancements and have led to various successful applications in fields such as engineering, mathematics, physics, biology, and other allied disciplines. Our main contribution is the development of a special function, specifically the confluent hypergeometric function (CHF) on the complex domain. By deriving various implementations of fractional order derivatives and integral operators using this function, we present a new class of special functions combining certain cases of Mittag-Leffler and confluent hypergeometric functions. Moreover, a new numerical technique for solving linear and nonlinear multi-order fractional differential equations has been developed using the proposed class of functions and the point collocation method. Graphical results are shown to demonstrate the efficacy of this proposed technique and its applicability.

Transport of heat in combustion engines, burners and consumption of energy via nuclear explosions is remarkably effected by magnetize nanofluid and radiation. Present attempt is relevant to the current Engineering applications; as design of heat exchangers, systems of renewable energy, and Nanotechnology. Therefore, main concern of the study is explored the radiative flux in Micropolar nanofluid flow under the Lorentz force and gravity modulation. The impacts of cross diffusion is also included in flow field. The mathematical model governing the flow are transformed into ODEs via similarity variables. The Keller box approach is utilized for numerical outcomes. A comprehensive analysis of the physical parameters is carried out, and numerical outcomes are displayed in graphical and tabular form. Obtained outcomes are compared with results that have already been published and found a good match. It has been found that temperature profile and concentration profile have a direct relation against Soret and Dufour respectively. Temperature profile and concentration profile has a direct relation against Dufour and Soret effects. Thermal field grows by enhancing radiation, Brownian motion and thermophoresis parameter. Furthermore, the skin friction.increases as the inclination factor grows up, but Nusselt and Sherwood numbers decline.

The process of formulating the basic strategies in a construction project must go through a set of stages. The desired objectives in feasibility studies should be highlighted to ensure that the packages of the infrastructure projects are moving smoothly in terms of the desired goal. In order to meet ambition for the long term in infrastructure projects, it is required to adopt the five pillars of SMART for rectifying the paths of feasibility studies. The study is a summarizing of fifteen elements that could have negative impacts on outputs of feasibility studies. The designed questionnaires have already been distributed via two stages to the experts/consultants in project management and others. 63 questionnaires were collected to find the negative impact of the elements, and the second stage included 89 participants for measuring their responses about the extent to which previous studies that were prepared over the past five years matched the concept of SMART-objectives. Based on the theoretical principle through analyzing the responses/opinions of participating experts, it was found that the feasibility studies for infrastructure projects obtained the following percentages: 46.07%, 41.57%, 28.09%, 22.47%, and 22.47%. This reflects that the objectives of the infrastructure project were specific, measured, achievable, relevant, and Time-Bound) in sequence consistent with the mentioned percentages. For the improvement outcomes of feasibility studies for infrastructure projects, that required a clear and invaluable link among all feasibility studies and the concept of applying the SMART-five pillars. Doi: 10.28991/HIJ-2024-05-03-05 Full Text: PDF

This research introduced a new method, the Aboodh Tamimi Ansari transform method ($ (AT)^2 $ method), for solving systems of linear and nonlinear fractional partial differential equations. The method combined the Aboodh transform method and the Tamimi Ansari method, allowing for the simultaneous solution of linear and nonlinear terms without restrictions. The Caputo sense was considered for fractional derivatives. The effectiveness of the proposed method was demonstrated through numerical solutions, graphical representations, and tabular data, showing strong agreement with exact solutions. The approach was deemed precise, easy to apply, and could be extended to address further challenges in fractional-order problems. Computational tasks were carried out using Mathematica 13.

Sami Abdulsalam Ali Hasan,1 Ibrahim Zaid Al-Shami,1 Mohsen Ali Al-Hamzi,1 Ghadeer Saleh Alwadai,2 Nada Ahmad Alamoudi,2 Saleh Ali Alqahtani,2 Arwa Daghrery,3 Wafa H Alaajam,4,5 Mansoor Shariff,6 Hussain Mohammed Kinani,7 Mohammed M Al Moaleem8 1Department of Conservative Dentistry, Faculty of Dentistry, Sana’a University, Sanaa, Yemen; 2Department: Restorative Dental Science, College of Dentistry, King Khalid University, Abha, Saudi Arabia; 3Department of Restorative Dental Sciences, College of Dentistry, Jazan University, Jazan, 45142, Saudi Arabia; 4Department of Restorative Dental Science, College of Dentistry, King Khalid University, Abha, Saudi Arabia; 5Department of Restorative Dentistry, Faculty of Dentistry, Sana’a University, Sana’a, Yemen; 6Prosthetic Department, College of Dentistry, King Khalid University, Abha, 62529, Saudi Arabia; 7Ministry of Health, Sabya General Hospital, Department of Dentistry, Jazan, Saudi Arabia; 8Department of Prosthetic Dental Science, College of Dentistry, Jazan University, Jazan, 45142, Saudi ArabiaCorrespondence: Mohammed M Al Moaleem, Department of Prosthetic Dental Science, College of Dentistry, Jazan University, Jazan, 45142, Saudi Arabia, Email malmoaleem@jazanu.edu.saBackground: To evaluate the radiant power of the light cure units (LCUs) in relation to their type, radiant exitance, number of years in clinical use, and condition of LCUs tips in governmental and public clinics in Dental Faculties in Sana’a City.Materials and Methods: LCUs were collected from different colleges at Sanaa City, Yemen, then LCU data as type, clinical age (< 1 year, between 1– 5 and ˃ 5-years), tip condition was visually inspected for damage and adhering debris, and the radiant exitance values of the tested LCUs. Radiant exitance values were subcategorized into three groups: < 400, 400– 850, and > 850 mW/cm², labeled as inadequate, marginal, and adequate radiant exitances, respectively. A Woodpecker radiometer was used with a mode lasting of 20 seconds was used with each LCU. Descriptive statistics of the different parameters were evaluated with SPSS version 25. One-way ANOVA and Mann–Whitney tests were performed to determine the mean difference between the groups with a significance value of ˂ 0.05 was considered.Results: Two hundred twenty-three LCUs were surveyed, and the majority were Light–emitting diode (LED). Forty-nine (21.9%), 117 (52.4%), 57 (25.6%) recorded lesser than, 400– 850, and more than 850 mW/cm², respectively. Radiant exitances of < year-old units were found to be higher than those of units used for ˃ 5 years with significant differences (p=0.001). The ANOVA test showed significant differences between the radiant exitance with clinical age and LCU tip conditions and a strong correlation p ˃ 0.050.Conclusion: LED curing lights were the most used in the tested Dental Faculties. More than half of the used LCU offered sufficient radiant exitance. Clinical age, the presence or absence of composite buildups, and damage to curing tips showed significantly affect radiant exitance values.Keywords: dental light cure, radiant exitance, contaminated tip, radiometer

This paper investigates the dynamics of a discrete-time predator-prey system in which the prey population is impacted by the Allee effect. Possible fixed points in the system are studied for their existence and topological categorization. Moreover, the presence and direction of period-doubling and Neimark-Sacker bifurcations at the interior fixed point are examined through the application of bifurcation theory and the centre manifold theorem. A hybrid approach is adopted to control chaotic behaviour and prevent bifurcations. Numerical examples are provided to substantiate our theoretical findings. The Allee effect has been shown to affect the dynamics of the system using numerical simulations. The moderate Allee effect stabilizes predator and prey populations, facilitating ecological cohabitation and persistence.

This manuscript presents enhanced versions of two methods: the natural transform iterative method (NTIM) and the q-homotopy analysis method (q-HAM). These methods harness concepts from Fractional Calculus, particularly leveraging the Caputo fractional derivative operator, to successfully manage the complexities of fractional-order systems. To validate their accuracy and efficiency, we applied the proposed techniques to FPDEs like the fractional-order KDV-Burger and fifth-order Sawada–Kotera equations. Our outcomes, which closely resemble the exact solutions, demonstrate how useful NTIM and q-HAM are for solving difficult FPDEs and improving the study of fractional calculus.

This study investigates the complex behavior of Jeffrey nanofluid flow in a porous oscillating microchannel under the influence of magnetohydrodynamic (MHD) effects. The research explores how magnetic field distortions lead to diverse accumulation patterns of nanofluid particles, a phenomenon attributed to homogeneous magnetization in fluid dynamics. Nanoparticles ranging from 0.25 % to 0.5 % (low and inexpensive concentrations) are remarkably consistent for best results in most machining procedures. Different concentrations of various nanomaterial's is utilized (φ1 = φ2 = 0.01, 0.02, 0.03, 0.04) to make the simple nanfluid and hybrid nanofluid suspensions. By employing fractal-fractional derivatives governed by power law, a mathematical model developed to describe the time-varying, compressible MHD flow of Jeffrey nanofluid. The model incorporates the effects of heat transfer, pressure, and magnetic fields on the fluid dynamics. A novel fractional approach utilizing the Laplace transform is applied to solve the fractal MHD hybrid-fluid model integrated into a porous medium. The study reveals velocity flow decrease with increasing Reynolds numbers but increase with channel inclination. Additionally, both the Darcy number and magnetic field orientation enhance heat transfer rates. In addition, the velocity profile enhanced by the hybrid nanofluid suspension as compared to simple nanofluid flow. The research validates its findings by demonstrating the convergence of fractional and numerical solution methods. Furthermore, the study compares the performance of different hybrid nanofluids, concluding that water-based (H2O + GO + MoS2) hybrid fluids exhibit slightly superior characteristics compared to (CMC + GO + MoS2) hybrid nanofluids.

Abstract Following the catastrophic 6 February 2023 Mw 7.8 and Mw 7.6 Kahramanmaraş earthquakes in the East Anatolian Fault Zone (EAFZ; southeast Türkiye), numerous aftershocks occurred along the major branches of this left‐lateral shear zone. The spatio‐temporal distribution of the earthquakes implied the stress‐triggering effects of co‐seismic ruptures on closely connected fault segments over large distances. On the 20 February 2023 two earthquakes with Mw 6.4 and Mw 5.2 struck Hatay (Türkiye) located near the Samandağ‐Antakya segment of the EAFZ. To understand the rupture evolution of these earthquakes, we first re‐located the aftershock sequence that occurred over a 3‐month period in the Hatay‐Syria region. A normal faulting mechanism with a significant amount of left‐lateral strike‐slip component at a shallow focal depth of 12 km was estimated for the 2023 Mw 6.4 earthquake from the inversion of seismological data. Our slip models describe a relatively simple and unilateral rupture propagation along about 36 km‐long active segments of the EAFZ. The co‐seismic horizontal displacements inferred from the Global Navigation Satellite System data are compatible with the oblique slip kinematics. Furthermore, we suggest that this earthquake did not produce notable tsunami waves on the adjacent coasts since the rupture plane did not extend to the seafloor of the Eastern Mediterranean with substantial amount of vertical displacement. We reckon that a future large earthquake (Mw ≥ 7.0) in the Hatay‐Syria region where increased stress was transferred to the fault segments of the EAFZ and the Dead Sea Fault Zone (DSFZ) after the 2023 earthquakes will be a probable source of tsunami at the coastal plains of the Eastern Mediterranean Sea region.

Abstract Solitary wave solutions are of great interest to bio-mathematicians and other scientists because they provide a basic description of nonlinear phenomena with many practical applications. They provide a strong foundation for the development of novel biological and medical models and therapies because of their remarkable behavior and persistence. They have the potential to improve our comprehension of intricate biological systems and help us create novel therapeutic approaches, which is something that researchers are actively investigating. In this study, solitary wave solutions of the nonlinear Murray equation will be discovered using a modified extended direct algebraic method. These solutions represent a uniform variation in blood vessel shape and diameter that can be used to stimulate blood flow in patients with cardiovascular disease. These solutions are newly in the literature, and give researchers an important tool for grasping complex biological systems. To see how the solitary wave solutions behave, graphs are displayed using Matlab.

Within the domain of nonlinear dynamics, the Belousov-Zhabotinsky reaction system has consistently captivated researchers, sustaining its position as a vibrant and dynamic area of exploration. As an enduring subject of study, the Belousov-Zhabotinsky system provides continuous opportunities to unravel the foundational tenets of nonlinear dynamics within intricate systems. In our quest to deepen comprehension of this complex system, we introduce an innovative methodology for addressing the time fractional Belousov-Zhabotinsky system. This novel approach leverages both the Natural Transform Iterative Method (NTIM) and the Optimal Homotopy Asymptotic Method (OHAM), aiming to contribute novel insights and methodologies to the ongoing discourse surrounding this intriguing and influential area of research. We obtained a series solution to test the accuracy of the suggested approach. The proposed technique has the advantage of requiring few calculations while producing high-precision results. To help you better understand, 2D and 3D graphical representations are provided to demonstrate the model's behavior and how changing the fractional order derivative in Caputo's sense and time affects the solutions.

Careful study of applied sciences and their development requires us to expand the scope of analytical studies. We aim during introducing the current manuscript to rediscover and present Grüss inequality in a new framework. In order to do that, we use the recently generalized proportional fractional integral operator for a certain function with respect to another continuous and strictly increasing function. Furthermore, we prove some new related inequalities using the current fractional integral operator. Some special cases of the presented results will be discussed.

The aim of this work is to provide a comprehensive analysis of the dynamics within an ecosystem characterized by interactions between prey and predators, through a combination of theoretical analysis and numerical simulation. The study investigates the impact of two pivotal effects: the “Hide-and-Escape” behavior exhibited by prey and the “Predation Skill Augmentation” strategy adopted by predators. Theoretical analysis identifies three equilibrium points, all of which show positive characteristics. Furthermore, local stability conditions are determined for each of these equilibrium points. The derivation of global stability conditions is also presented, and their validity and importance as local stability conditions for the coexistence point are demonstrated. In addition, Kolmogorov conditions for coexistence and extinction are verified, as well as local bifurcation analysis. For the validity of the results, a numerical simulation of the system using MATLAB is conducted.

نفذ البحث في مخبر الحشرات التابع لقسم وقاية النبات في كلية الهندسة الزراعية، جامعة تشرين، سورية، ضمن ظروف مخبرية محكمة خلال العام 2022، حيث استخدمت ثمار القرع العسلي Cucurbita moschata كنبات عائل لهذه الحشرة، وتمت العدوى بالآفة من أشجار حمضيات مصابة على شكل إناث تحتوي بيوض (طور العدوى). هدف هذا البحث إلى دراسة المؤشرات الحياتية وإعداد جدول حياة للمتطفل(Hymenoptera: Pteromalidae) Scutellista caerulea، عند درجات حرارة ثابتة (20، 25، 30 °س)، ورطوبة هواء نسبية (%5±65) وفترة إضاءة 8:16 سا (إضاءة : ظلام)، حسبت المؤشرات الحياتية للمتطفل S.caeruleaباستخدام برنامج (TWOSEX-MS Chart) وأظهرت النتائج أن أعلى قيمة لمعدل التعويض الصافي (R0) 5.73 عند درجة حرارة 25 °س ، والمعدل النهائي للتزايد (λ) 1.04 عند درجة حرارة 30 °س، وأقصر مدة للجيل ( T) 35.22 يوماً عند درجة حرارة 30 °س ، كما بلغت أعلى قيمة للخصوبة للمتطفل11.6 عند درجة حرارة 25 °س ، وكان خروج البالغات ومعدل الحياتية هو الأعلى عند درجة الحرارة 30°س حيث بلغت52% لطور الأنثى و 58% لطور الذكر البالغ.

A number of thermal devices might benefit from the usage of nanofluids in solar power. In this research, the idea of MHD mixed convective hybrid nanofluids including grapheme oxide (GO) and molybdenum disulfide (MoS2) nanoparticles with water (H2O) and Carboxymethyl Cellulose (CMC) as base fluids in a perpendicular channel to analyze the heat transfer of the flowing fluid with the help of recent definition of fractional derivatives namely Fractal fractional derivative. The problem is expressed as PDEs with beginning and boundary conditions, and it is analyzed analytically using the Laplace transform method. The velocity, temperature, and concentration measurements are also shown in series for their appropriate Laplace inverse. Delays in parameters like nanoparticle volume sharing rate have a significant influence on these techniques. Skin friction, Nusselt, and Sherwood numbers are computed for the longitudinal channel's left and right walls, and the necessary numerical results are presented in tabular format. As a result, it is discovered that the rate of heat transfer reduces as the volume percentage of nanoparticles and the Fractal time fractional value rise. Furthermore, when comparing nanofluids, water-based (H2O + GO + MoS2) hybrid nanofluids have a greater influence on governed model than (CMC + GO + MoS2)-based hybrid nanofluids.

This study aims to examine the early detection and treatment of conjunctivitis (eye infection) through vaccination and recovery measures, both with and without medication. We develop an immune system-boosting mathematical model and convert it to a fractionally ordered model using the ABC operator. Key properties, such as the uniqueness and boundedness of the model, are investigated using Banach space. To assess the stability of the newly developed SEVIRuRi system and confirm the occurrence of flip bifurcation, we conduct both qualitative and quantitative analyses. We calculate the basic reproductive number, R0, using an advanced approach and analyze its impact across different sub-compartments. Sensitivity analysis is performed on each parameter to understand the rate of change sensitivity. The Atangana–Toufik method is employed to solve the system for various fractional values, providing a reliable bounded solution. Simulations are conducted to observe the real behavior and effects of the conjunctivitis virus, showing that individuals with a strong immune system can recover with or without medication. Finally, we determine the actual state of virus control post-early detection, accounting for treated and untreated individuals due to the robust immune system and precautionary measures.

The primary focus of this paper is to thoroughly examine and analyze a class of a fractional quadratic integral equation via generalized fractional integral. To achieve this, we introduce an operator that possesses fixed points corresponding to the solutions of the fractional quadratic integral equation, effectively transforming the given equation into an equivalent fixed-point problem. By applying the Banach fixed-point theorems, we prove the uniqueness of solutions to fractional quadratic integral equation. Additionally, The Adomian decomposition method is used, to solve the resulting fractional quadratic integral equation. This technique rapidly provides convergent successive approximations of the exact solution to the given fractional quadratic integral equation, therefore, we investigate the convergence of approximate solutions, using the Adomian decomposition method. Finally, we provide some examples, to demonstrate our results. Our findings contribute to the current understanding of fractional quadratic integral equation and their solutions and have the potential to inform future research in this area.

The study aims to obtain new approximate analytical solutions for the fractional order nonlinear Foam Drainage equation through a novel modification of the well-known Optimal Auxiliary Functions Method (OAFM). This method systematically constructs auxiliary functions, and by optimizing their parameters, it provides approximate solutions closely mirroring the original behavior of the problem. Numerical simulations, presented in tabular form, demonstrate the effectiveness of the proposed approach. Graphical representations of the solutions are utilized to further validate the applicability and accuracy of the suggested technique. Additionally, the results affirm that the modified OAFM stands out as one of the most effective tools for addressing nonlinear problems in the field of science and technology, thereby contributing valuable addition to the field.

The photosynthetic activity of phytoplankton in the seas is responsible for an estimated 50–80 % of the world's oxygen generation. Both phytoplankton and zooplankton require some of this synthesized oxygen for cellular respiration. This study aims to better understand how the oxygen-phytoplankton dynamics are altered due to the Allee effect in phytoplankton development, particularly when considering the time-dependent oxygen generation rate. The dynamic analysis of the model is dedicated to finding the possible equilibrium points. The analysis reveals that three equilibrium points can be obtained. The stability study demonstrates that one of the equilibrium points is always stable. The remaining equilibrium points are stable under specific conditions. We also identify bifurcations originating from these equilibrium points, including transcritical, pitchfork, and Hopf bifurcation. We derive conditions for stable limit cycles (supercritical Hopf bifurcation) and, in some cases, establish the non-existence of solutions. Numerical simulations are performed to validate our theoretical findings. Furthermore, it is noted that the Allee threshold for the phytoplankton population (k0) significantly influences the overall dynamics of the system. When k0≤0.001, the population of plankton is at risk of extinction. On the other hand, when 0.001

This study investigates the impact of coupled heat and mass transfer on the peristaltic migration of a magnetohydrodynamic (MHD) stress-strain Jeffery-type hybrid nanofluid flowing through an inclined asymmetric micro-channel with a porous medium. The fundamental two-dimensional momentum and energy transport equations are simplified under the assumptions of long wavelength and low Reynolds number. To solve the momentum and heat transfer problems, two advanced fractional derivative approaches are employed: the fractal integral and the Prabhakar fractional derivative. The pressure difference is determined using numerical integration techniques, such as the Stehfest and Tzou's algorithms. The results are presented through graphs and tables, which illustrate the effects of various parameters on the velocity, heat transfer, and trapping phenomena. As a result, we concluded that, pressure gradients grow with higher Reynolds numbers and channel-inclined angles. The heat transfer rate is observed to decrease as the Darcy number and the orientation of the electromagnetic field increase. When comparing the fractional derivative approaches, the fractal operator exhibits a more significant impact on the momentum profiles compared to the Prabhakar fractional operator. This difference is attributed to the distinct characteristics of the integral kernels associated with each fractional derivative definition. Furthermore, when comparing hybrid nanofluids, water-based (H2O + Ag + TiO2) hybrid fluids have a somewhat more significant effect than (C6H9NaO7 + Ag + TiO2) hybrid nanofluids.

مقدمة: يعد اليرقان عند حديثي الولادة مرضاً شائع الانتشار وسبباً هاماً للاستشفاء والتدخل الطبي. تعد المعالجة الضوئية الخيار الأول والأكثر استخداماً في المعالجة الطبية لليرقان. تميل الدراسات الحالية لاستخدام المعالجة الضوئية المتقطعة بدلا ًمن المستمرة للتقليل من الآثار الجانبية غير المرغوبة للمعالجة الضوئية. الهدف: دراسة فعالية المعالجة الضوئية المتقطعة مقارنة بالمعالجة الضوئية المستمرة لعلاج فرط بيليروبين الدم غير المقترن عند حديثي الولادة. الطرائق: دراسة رصدية تحليلية أجريت على 63 وليداً في مشفى تشرين الجامعي -اللاذقية خلال الفترة من آب 2022 وحتى تشرين الأول 2023. تم تقسيم المرضى إلى مجموعتين: مجموعة A تلقت معالجة ضوئية متقطعة (2ساعة وصل/1 ساعة قطع) ومجموعة B تلقت معالجة ضوئية مستمرة وذلك لمدة 12 ساعة، وتمت معايرة قيم بيليروبين المصل الكلي عند الاستشفاء وبعد 6و12 ساعة من المعالجة الضوئية. النتائج: كانت القيم المتوسطة لبيليروبين المصل الكلي عند القبول 16.6±1.39 mg/dlللمجموعة A و16.6±1.34 mg/dl للمجموعة B. بعد 6 و12 ساعة من المعالجة الضوئية كانت القيم المتوسطة لبيليروبين المصل الكلي 15.7±0.4 mg/dl, 13.7±1.33mg/dl للمجموعة A و15.5±0.7mg/dl, 13.5±1.22mg/dl للمجموعة B على التوالي. لم يكن هناك أي فرق هام إحصائي بين المجموعتين بالنسبة لقيم بيليروبين المصل الكلي (P-value˃5%). الخلاصة: العلاج الضوئي المتقطع يكافئ فعالية العلاج الضوئي المستمر في علاج فرط بيليروبين الدم غير المقترن عند حديثي الولادة.

Abstract Salmonella Typhi, a bacteria, is responsible for typhoid fever, a potentially dangerous infection. Typhoid fever affects a large number of people each year, estimated to be between 11 and 20 million, resulting in a high mortality rate of 128,000 to 161,000 deaths. This research investigates a robust numerical analytic strategy for typhoid fever that takes infection protection into consideration and incorporates fuzzy parameters. The use of fuzzy parameters acknowledges the variation in parameter values among individuals in the population, which leads to uncertainties. Because of their diverse histories, different age groups within this community may exhibit distinct customs, habits, and levels of resistance. Fuzzy theory appears as the most appropriate instrument for dealing with these uncertainty. With this in mind, a model of typhoid fever featuring fuzzy parameters is thoroughly examined. Two numerical techniques are developed within a fuzzy framework to address this model. We employ the non-standard finite difference (NSFD) scheme, which ensures the preservation of essential properties like dynamic consistency and positivity. Additionally, we conduct numerical simulations to illustrate the practical applicability of the developed technique. In contrast to many classical methods commonly found in the literature, the proposed approach exhibits unconditional convergence, solidifying its status as a dependable tool for investigating the dynamics of typhoid disease.

AbstractThis paper introduces a new modification to an iterative method for solving Cauchy problems (IVPs) based on an inverse polynomial technique. The proposed method is proven to be consistent, stable, and convergent. We also demonstrate the consistency property of the One-stage scheme and the Two-stage scheme, as well as the stability property of the proposed method. To validate the accuracy of our approach, we conduct several numerical experiments and present the results graphically. Our findings show that the proposed method outperforms existing approaches in terms of accuracy and efficiency. Additionally, we discuss the implications of our results for future research in this field. Overall, this paper provides a valuable contribution to the numerical solution of IVPs and lays the groundwork for further exploration in this area.

In this paper, we propose an effective numerical method to solve the one- and two-dimensional time-fractional convection-diffusion equations based on the Caputo derivative. The presented approach employs a hybrid method that combines Lucas and Fibonacci polynomials with the Caputo derivative definition. The main objective is to transform the problem into a time-discrete form utilizing the Caputo derivative technique and then approximate the function's derivative using Fibonacci polynomials. To evaluate the efficiency and accuracy of the proposed technique, we apply it to one- and two-dimensional problems and compare the results with the exact as well as with existing methods in recent literature. The comparison demonstrates that the proposed approach is highly efficient, accurate and ease to implement.

In the present work, Einstein's vacuum field equation is investigated analytically to explore the solitary wave solutions. This equation arises in mathematical physics, having meaningful applications in the general theory of relativity. This concept is crucial for numerous challenging experiments and space missions. The generalized exponential rational function and modified auxiliary equation approaches are used to obtain the exact solitary wave solution. Various types of solutions are extracted, including exponential functions, hyperbolic functions, trigonometric functions, and rational forms. Additionally, a stability analysis for the Einstein vacuum field equation is conducted. Appropriate parameters are chosen to draw 3-D and corresponding contour plots of some solutions, which clearly demonstrate the solitary wave behaviors. The obtained results support the idea that applying these approaches is the most effective strategy for resolving any nonlinear issues that may arise in science and technology.

Mathematical formulations are essential tool to show the dynamics that how various diseases spread in the community. Differential equations with fractional or integer order can be utilized to see the effect of the dynamics direct or indirect Leptospirosis transmission, which are analyzed with different aspects. A mathematical description and dynamical sketch of Leptospirosis with environmental effects have been studied as a result of the successful efforts of various writers. In this study, we analyzed the Leptospirosis model described using a nonlinear fractional-order differential equation that takes the environmental effects into consideration. The proposed fractional order system is investigated qualitatively as well as quantitatively to identify its stable position. Local stability of the Leptospirosis system is verified and test the system with flip bifurcation. Also system is investigated for global stability using Lyapunov first and second derivative functions. The existence, boundedness and positivity of the Leptospirosis is checked, which are the key properties for such of type of epidemic problem to identify reliable findings. Effect of global derivative is demonstrated to verify its rate of effects according to their sub-compartments. Solutions for fractional order system are derived with the help of advanced tool fractal fractional operator for different fractional values. Simulation are carried out to see symptomatic as well as a asymptomatic effects of Leptospirosis in the world wide, also show the actual behavior of Leptospirosis which will be helpful to understand the outbreak of Leptospirosis with environmental effects as well as for future prediction and control strategies.

Contracting cancer typically induces a state of terror among the individuals who are affected. Exploring how glucose excess, estrogen excess, and anxiety work together to affect the speed at which breast cancer cells multiply and the immune system’s response model is necessary to conceive of ways to stop the spread of cancer. This paper proposes a mathematical model to investigate the impact of psychological panic, glucose excess, and estrogen excess on the interaction of cancer and immunity. The proposed model is precisely described. The focus of the model’s dynamic analysis is to identify the potential equilibrium locations. According to the analysis, it is possible to establish four equilibrium positions. The stability analysis reveals that all equilibrium points consistently exhibit stability under the defined conditions. The transcritical bifurcation occurs when the glucose excess is taken as a bifurcation point. Numerical simulations are employed to validate the theoretical study, which shows that psychological panic, glucose excess, and estrogen excess could be significant contributors to the spread of tumors and weakness of immune function.

In the current scenario of the need for cost-effective remediation, our study aimed to assess the remedial potential of bacteria obtained from metal-rich wastewater. To simulate the conditions, we prepared wastewater containing five toxic metals (Cu, Cr, Ni, Fe, and Pb). Two types of metal-resistant bacteria were isolated from a prominent wastewater drain in Lahore, Pakistan. These isolated bacteria were thoroughly characterized, both phenotypically and genotypically. Subsequently, the isolated bacteria were exposed to the wastewater solution containing each of the aforementioned metals at a concentration of 250 ppm. The exposed isolates were then incubated for a duration of 15 days. After 5 days, we measured the uptake of metals by the bacterial isolates. Following the 15-day incubation period, we observed that the bacterial isolates demonstrated the maximum efficiency in removing metals, with approximately 47.5% of Fe, 77% of Ni, 75.75% of Cu, 64% of Cr, and 82.5% of Pb being removed. These findings have significant implications for the development of environmentally friendly and cost-effective strategies for metal ion remediation. HIGHLIGHTS Assess the remedial potential of bacteria obtained from metal-rich wastewater.; Isolated bacteria were thoroughly characterized, both phenotypically and genotypically.; Bacterial isolates demonstrated maximum efficiency in removing metals, with approximately 47.5% of Fe, 77% of Ni, 75.75% of Cu, 64% of Cr, and 82.5% of Pb being removed.;

Engineers have recently become attracted to electrically conducting nanofluids (NFs) due to various applications in several applied science and engineering disciplines. They have been employed in magnetic refrigeration, cancer treatment (hyperthermia), medicine, and magnetic resonance imaging, among other things. Considering the importance of electrically conducting NFs, in this article, we have proposed a fractionalized MHD (Magnetohydrodynamics) and thermal transmission of a Brinkman-type tri-hybrid nanofluid over an infinite plate saturated through a porous medium with generalized velocity and ramped conditions. For the solution of the governed fractional model, we have utilized a recent definition of fractional derivatives, known as Atangana-Baleanu (AB) fractional derivative and Laplace transformation. The computational results are exhibited for tri-hybrid (TiO2-Al2O3-CuO/H2O) NF and described through graphical diagrams and tables to discover the physics of numerous relevant flow parameters on temperature and velocity profiles. It is detected that both thermal transmission and momentum profile for tri-hybrid NF is a better technique as compared to hybrid NF and NF for both graphical and numerical comparisons.

Minerals and nutrients are vital to life, but their excess can harm health and sometimes lead to life risks. Harmful impact of nutrients in water can be a threat to marine life as well. Waquoit Bay linked with its eight rivers and ponds is becoming the reason for excess nutrient passage into the Bay. Excess amounts of nutrients were found in Waquoit Bay from coastal areas and therefore analyzed in this work by a system of nine differential equations. The main objective of this paper is to develop a mathematical model to assess the situation of pollution in Waquoit Bay and suggest some solutions using optimal control theory with Hamiltonian system. Mathematical Model of water pollution will be evaluated numerically, with different input models to track environmental contamination in a water body. To prove the accuracy of this model, its numerical results will be compared with real data and the impact of control strategies i.e. nutrient control from housing area and bio dredging will be studied. Benefit of developing such mathematical models can be a decision support for planning restrictions in coastal areas near Waquoit Bay.

The optimization of the vaccination campaign and medication distribution in rural regions of Morocco conducted by the Ministry of Health can be significantly improved by employing metaheuristic algorithms in conjunction with a tour planning system. This research proposes the utilization of six metaheuristic algorithms: genetic algorithm, rat swarm optimization, whale optimization, spotted hyena optimizer, penguins search optimization, and particle swarm optimization, to determine the most efficient routes for equipped trucks carrying vaccines and medications. These algorithms consider critical field constraints, such as operating hours of vaccination centers, vaccine availability, and distances between centers while minimizing the overall journey duration. In addition, a comprehensive tour planning system is integrated into the optimization framework accounting for transportation costs such as fuel expenses and truck maintenance costs. By incorporating these factors, the Ministry of Health aims to achieve the maximum efficiency while minimizing the financial burden associated with the vaccination campaign in rural areas. The integration of metaheuristics and the tour planning system presents a robust and data-driven solution for the Ministry of Health to enhance the effectiveness of their vaccination and medication distribution campaigns in rural regions of Morocco. This approach not only minimizes costs but also improves overall efficiency by ensuring timely access to vaccines and medications for the rural population. The findings of this research contribute to the growing body of knowledge in the field of healthcare logistics optimization and provide valuable insights for policymakers and practitioners involved in similar campaigns worldwide.

The 6 February 2023 M_w 7.8 Pazarcık and subsequent M_w 7.5 Elbistan earthquakes generated strong ground shaking that resulted in catastrophic human and economic loss across south‐central Türkiye and northwest Syria. The rapid characterization of the earthquakes, including their location, size, fault geometries, and slip kinematics, is critical to estimate the impact of significant seismic events. The U.S. Geological Survey National Earthquake Information Center (NEIC) provides real‐time monitoring of earthquakes globally, including rapid source characterization and impact estimates. Here, we describe the seismic characterization products generated and made available by the NEIC over the two weeks following the start of the earthquake sequence in southeast Türkiye, their evolution, and how they inform our understanding of regional seismotectonics and hazards. The kinematics of rupture for the two earthquakes was complex, involving multiple fault segments. Therefore, incorporating observations from rupture mapping was critical for characterizing these events. Dense local datasets facilitated robust source characterization and impact assessment once these observations were obtained and converted to NEIC product input formats. We discuss how we may improve the timeliness of NEIC products for rapid assessment of future seismic hazards, particularly in the case of complex ruptures.

Abstract This research aims to attain the optimal method of removing the high salinity concentrations without its effect on the balance or accuracy of stable isotopes measurement of deuterium and oxygen-18 (δ18O, δ2H). Four treatment methods (i.e., distillation, vacuum distillation, electro dialysis and ion exchange) were applied for nine samples, which were obtained from different water sources (sea, groundwater, river).l Worth to notice that the samples have Electrical Conductivity (EC) ranged (1000–60,000 µs/cm). Liquid–Water Isotope Analyzer used to measure the isotope concentration of δ18O, δ2H. The research findings of the four applied methods revealed their effectiveness with various percentages (normal distillation: 92.37%; vacuum distillation: 88.31%; electro dialysis: 94.85%; ion exchange: 99.62%). In addition, the investigation was conducted a clear correspondence measurement of (δ18O, δ2H) isotopes before and after treatment. The four methods results indicated that samples with EC ranged (1000–5000 µs/cm) have no effect on stable isotope readings. Whereas, samples with EC higher than 10,000, have substantial influence on the stable isotope readings. Finally, vacuum distillation method attained the best results among the treatment methods for EC ranged (10,000–60,000 µs/cm) without affecting the isotopic content of (δ18O, δ2H). There is a clear correspondence of the stable isotopic measurements before and after treatment, for all the selected samples.

This current work presents a comparative study of the fractional-order Cahn-Allen (CA) equation, where the non-integer derivative is taken in the Caputo sense.The Cahn-Allen equation is an equation that assists in the comprehension of phase transitions and pattern formation in physical systems. This equation describes how different phases of matter, such as solids and liquids, change and interact throughout time. We employ two analytical methods: the Laplace Residual Power Series Method (LRPSM) and the New Iterative Method (NIM), to solve the proposed model. The LRPSM is a combination of the Laplace Transform and the Residual Power Series Method, while the New Iterative Method is a modified form of the Adomian Decomposition Method that does not require any type of polynomial or digitization. For the purpose of accuracy and reliability, we compare our findings with other methods and the exact solution used in the literature. Additionally, 2D and 3D plots are generated for various fractional order values denoted as p. These plots illustrate that as the fractional order p approaches 1, the graph of the approximate solution gradually coincides with the graph of the exact solution.

This scientific study investigates to check the dynamical behavior of yellow virus in red chilli with fractional order techniques. While attempts are being made to stop the yellow virus pandemic, a more infectious yellow virus found in red chilli is developing in many locations. It is crucial to learn how to create strategies that will stop the yellow virus’s spread to mimic the propagation of the yellow virus in red chilli plants while maintaining a specific degree of immunity. As a case study, we looked at the possibility of an outbreak in red chilli plants. Recently, novel fractal-fractional operators proposed by Atangana have been widely used to observe the unanticipated elements of a problem. Currently, the illness caused by the yellow virus in red chilli is common and difficult to treat. The inventive operators have been implemented in this structure to observe the influence of vaccination on the yellow virus in the red chilli model using a variety of values for υ1 and υ2 which are utilized to represent the impact of vaccination. The number of reproductions will determine whether the system is clear of sickness. Using the fractal-fraction Mittag–Leffler operator, we examined the qualitative and quantitative characteristics of the yellow virus in the red chilli model. The results of the fixed point theory are used to apply an improved method for the fractional order model of the yellow virus. Nonlinear analysis was used to assess the stability of the Ulam-Hyres. Numerical simulations are demonstrated to prove the efficiency of the proposed method. The tools employed in this model appear to be quite potent and capable of simulating the expected theoretical conditions in the issue.

Oral literature is a part of folklore that is the legacy of fictional and non-fictional traditions of the past people. has taken. There are many critiques today that are based on structural functions. Structuralists have always sought to find patterns in which to examine stories. Among narrators, Greimas has a particular interest in popular literature, which is applicable to Kurdish motifs. The purpose of this study is to study the myths, stories and Kurdish myths of Ilam based on Greimas theory. Due to the lack of scientific study and the need for a structural study and the great reputation of this theory, an attempt has been made to answer this main question, what is the representation of the study of Elamite myths, tales and motels based on Greimas theory. To answer the questions, 127 motels were selected from 5 books using the library method and then evaluated with the pattern of double confrontations and triple chains of Greimas. The result of this study indicates the existence of six actors in motels. Thirteen groups can be identified in terms of the presence or absence of characters. In some stories, one or more actors are absent, with the sender having the highest frequency in this regard. In the classification of character types, men are the most used and creatures are the least used. Greimas narrative chains are also seen in all motels.

Background: Anemia is a common issue in chronic leukemia, which results in a worse outcome and shorter survival. Inadequate production of erythropoietin (EPO) as compared to the severity of anemia may play a major role in ACD for patients with hematological malignancies. Clarifying the role of EPO may provide a better understanding of its pathogenesis, and proper management of patients. Objectives: To determine serum EPO levels and look for any potential link between EPO and the cause of anemia in anemic patients with chronic leukemia in a sample of Iraqi patients in the middle euphrates region. Materials and Methods: This is a case control study included 38 patients (19 chronic myeloid leukemia [CML], 19 chronic lymphocytic leukemia [CLL]) who were attending the outpatient clinic of hematology in Baghdad Teaching Hospital, Marjan Teaching Hospital from September 2022 to March 2023, together with 30 adult participants without disease as a control group. All patients involved were diagnosed as having a disease based on a specialist’s physical examination, morphological evaluation of peripheral blood films and bone marrow, and flow cytometric immune-phenotypic profile. Blood samples were collected from each subject, and the following investigations were done: CBC, RFT, blood film examination, and ELISA assay for serum EPO. Results: The mean age of CML patients was (50.1 ± 12.85) range from 24 to 72, CLL patients (58.2 ± 10.4) range from 38 to 75. The majority of patients were men (N = 23, 60.5%). The participants in the patient group were subdivided into 18 (47.4%) patients with anemia and 20 (52.6%) patients without anemia. The mean differences of EPO concentration (U/L) between study groups demonstrated significant higher level among patient group (49.53 ± 56.82) than control group (12.73 ± 4.72) with P value < 0.0001. The level of serum EPO in anemic patients (89.28 ± 61.95) has been found to be higher than non-anemic patients (13.82 ± 4.43) and it was statistically significant (P < 0.0001). Endogenous EPO production was found to be defective in 10% of CML patients, 50% of CLL patients were judged by a value for the ratio of observed-to-predicted serum EPO levels (observed/predicted ratio) of ≤0.9. Conclusion: These findings indicate that anemia associated with hematologic malignancy may result from an inappropriately low EPO response. EPO treatment should benefit in this group of patients.

Brucellosis is an endemic zoonotic disease caused by intracellular gram-negative coccobacilli called Brucella. This infectious disease may implicate many farm animals and is transmissible to exposed humans. Brucellosis is potentially life-threatening and may lead to granulomatous multi-organ involvement with tendency to chronicity and recurrence. The treatment of brucellosis requires combined and protracted antimicrobial therapies to eliminate the disease and to avoid its relapse. Genitourinary brucellosis is common among infected humans in endemic areas and is considered the second-most affected focal site, which commonly manifests as epididymo-orchitis. Testicular abscess, however, is an extremely rare complication of brucellosis. To the best of our knowledge, in the literature, there are to date only 16 previously published case reports, including 22 patients of brucellar testicular abscesses, emphasizing the extreme rarity of this condition. Most of these cases harbored small abscesses, which were treated conservatively using antibiotics therapy only, or with added drainage of the abscesses. Larger abscesses were reported to necessitate orchiectomy. In some cases, the abscesses were mimicking tumors, and surgeries for orchiectomy were done accordingly. A summary of the previously reported cases in the literature is presented. Here, we present the 17th case report of a 34-year-old man with a right-side huge multilocular brucellar testicular abscess apparently replacing the entire testicle, who was successfully treated with organ-sparing management by incision-drainage of the large abscess with antibiotics, to eventually preserve his testis. In conclusion, brucellosis should be considered among the differential diagnoses of any testicular swelling, especially in endemic areas. Drainage of brucellar testicular abscess with appropriate medical treatment is feasible and may preserve the testicle, even with large abscess apparently replacing the entire testicle.

The fractional derivative is an advanced category of mathematics for real-life problems. This work focus on the investigation of 2nd wave of the Corona virus in India. We develop a time-fractional order COVID-19 model with effects of the disease which consist of a system of fractional differential equations. The fractional-order COVID-19 model is investigated with Atangana-Baleanu-Caputo fractional derivative. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. The fractional-order system is analyzed qualitatively as well as verified sensitivity analysis. Fixed point theory is used to prove the existence and uniqueness of the fractional-order model. Analyzed the model locally as well as globally using Lyapunov first and second derivative. Boundedness and positive unique solutions are verified for the fractional-order model of infection of disease. The concept of fixed point theory is used to interrogate the problem and confine the solution. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease on society. Simulation has been made to understand the behavior of the virus.

This research study evaluates the use of a supercapacitor module as a fast-response energy storage unit to improve energy self-consumption and self-sufficiency for renewable energy systems applications. The designed system consists of the photovoltaic component with 3.0 kWp capacity combined with (0–5) supercapacitor module with a capacity of 500F-2.7V per module to serve the desired load. The analysis was carried out using experimental data for the electrical load and solar irradiance, as well as ambient temperature at a 1-minute temporal resolution for the year 2020. The measured daily average power of the electrical load was 0.299 kW, with a daily energy consumption of 7.2 kWh/day at a maximum peak of 5.36 kW, while the yearly energy consumption was recorded 2620 kWh/year. The measured daily average solar irradiance was 3.1 kWh/m2/day, and the monthly average ambient temperature was 10.7 °C.The charge of the supercapacitor was only possible from the photovoltaic system and not from grid. The simulation results demonstrated that the use of the supercapacitor module could feed the rapid peaks of electrical load and significantly increase energy self-consumption and self-sufficiency. Using only five supercapacitor modules increases the annual self-consumption from 21.75% to 28.74% and the percentage of self-sufficiency increases from 28.09% to 40.77%. The study concluded that adding small and responsive energy storage is an excellent choice of batteries.

Good culture in Islam is often called fastabiqul khoirot which means competing or competing for good. This kind of culture must be owned by everyone including in an institution if they want their institution to develop well. This study aims to describe the steps or strategies of the Head of Madrasah to stimulate or awaken Fastabiqul Khoirot culture and analyze several factors in its application. The research method uses Descriptive-Qualitative studies. Data collection using observation, interview and documentation methods. The object of research is at MAN Batu City. Results found: 1) The strategy of the Head of Madrasah includes: Divide clear tasks for each element, respect every constructive opinion or proposal from each element, reward every achievement achieved, and build a winning mentality and unyielding attitude. 2) The analysis from the Head of Madrasah about the factors that become obstacles and solutions include: Newly recruited teachers and education staff have not been able to carry out jobdis optimally, so the school must provide assistance, all elements on average are still shy in submitting an idea or proposal about school development, the solution is that the Head of Madrasah approaches with a persuasive approach, there is still envy between members to continue to compete, There is no effective solution, and constrained by the assumption that the task is a burden that results in discouragement if the task is not successfully done, the solution builds motivation with direction and example to change someone's main said about it.

In recent years, the coronavirus (COVID-19) spread in a dangerous and rapidly. It first appeared in the Chinese city of Wuhan in early December 2019, causing many cases of infection and death because of the rapid spread of the virus throughout the world. The conversion of patient information from paper to electronic helps the medical staff and researchers analyze and retrieve information faster. In this paper, we gathered data about patients infected with COVID-19 who were registered in the Iraqi hospitals of two governorates (Diwaniyah and Najaf) from 2020 to 2023. In addition, we used machine learning algorithms that protect the infection of the data entered for the patient. The highest accuracy (average in both datasets od Diwaniyah and Najaf) ) are achieved by both the algorithms Nave Bayes (90%) and Decision tree (90%) , while the K nearest neighbor (89%), Random forest() and artificial neural network (84).

This paper investigates the dynamic behavior of cracked Rayleigh beams constructed from bidirectional functionally graded (BDFG) materials under simple boundary conditions. A torsional massless spring is employed to model the beam's open crack type. The vibration equations are obtained using Hamilton's principle. The graded beam material properties are varied throughout the thickness based on the power-law distribution and in the longitudinal direction using the exponential material distribution. To solve the dynamic equations, Galerkin's approach is employed. The paper evaluates the impacts of the axial index, gradient property index, beam modulus ratio, and crack parameters on the natural frequencies of the FG beam. The results indicate that the dimensionless natural frequencies of intact graded beams decrease with increased gradient index k. In contrast, they increase with a rise in the modulus ratio. Additionally, the results demonstrate that an increase in the crack depth ratio decreases dimensionless natural frequencies.