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Theoretical research has numerous challenges, particularly about modeling structures, unlike experimental analysis, which explores the mechanical behavior of complex structures. Therefore, this study suggests a new model for functionally graded shell structures called “Tri-coated FGM” using a spatial variation of material properties to investigate the free vibration response incorporating the porosities and microstructure-dependent effects. Two types of tri-coated FG shells are investigated, hardcore and softcore FG shells, and five distribution patterns are proposed. A novel modified field of displacement is proposed by reducing the number of variables from five to four by considering the shear deformation effect. The shell is rested on a viscoelastic Winkler/Pasternak foundation. An analytical solution based on the Galerkin approach is developed to solve the equations of motion derived by applying the principle of Hamilton. The proposed solution is addressed to study different boundary conditions. The current study conducts an extensive parametric analysis to investigate the influence of several factors, including coated FG nanoshell types and distribution patterns, gradient material distribution, porosities, length scale parameter (nonlocal), material scale parameter (gradient), nanoshell geometry, and elastic foundation variation on the fundamental frequencies. The provided results show the accuracy of the developed technique using different boundary conditions.

Bessel function has a significant role in fractional calculus having immense applications in physical and theoretical approach. Present work aims to introduce fractional integral operators in which generalized multi-index Bessel function as a kernel, and develop some important special cases which are connected with fractional operators in fractional calculus. Here, we construct important links to familiar findings from some individual occurrence with our key outcomes.

Abstract The fractional Hopfield neural network (HNN) model is studied here analyzing its symmetry, uniqueness of the solution, dissipativity, fixed points etc. A Lyapunov and bifurcation analysis of the system is done for specific as well as variable fractional order. Since a very long time ago, HNN has been carefully studied and applied in various fields. Because of the exceptional non-linearity of the neuron activation function, the HNN system is stoutly non-linear. Chaos control using adaptive SMC considering disturbances and uncertainties is done about randomly chosen points by designing suitable controllers. Numerical simulations performed in MATLAB verify the efficacy of the designed controllers.

The control of the novel five-dimensional hidden attractors hyperchaotic system is investigated. We suggest an approach to change the model of its hyperchaotic behavior to an unpredictable trivial fixed point employing the stability principle. We are also researching the synchronization of the same system, focusing on the stability theory. Numerical simulations show that effective control and synchronization results are obtained with the control method.

Reliability is one of the important factors in production inventory system as well as in the demand of the products. During a production process, the products which are more perfect with higher reliability increase the demand of the product whereas credit facility is also one of the popular business strategies. Combining these two concepts in together, we have described and analyzed mathematically a production inventory model with a partial credit facility and the reliability effect on the production system in which the customers’ demand is dependent on the price of the products and deterioration rate is considered to be constant. In this proposed model, trade credit policy on both the manufacturer and customers is introduced by taking into account all the possible situations on the basis of allowed credit periods. Under these situations, taking all possible cases for the manufacturer credit period as well as customers’ credit period, seven non-linear optimization problems for the proposed model are obtained. Since the corresponding optimization problems associated to this model are highly non-linear, we have found closed form optimal solution of the corresponding each of these objective functions by using Taylor’s series approximation technique. The convexity of the objective function of each non-linear problem is also investigated graphically. Finally, to validate the proposed model a set of seven numerical examples have been simultaneously solved and a sensitivity analysis is executed to notice the behavior of the parameters on the optimal solution.

This paper extends the concept of dissipativity to a new class of dynamical systems known as negative imaginary systems. The paper also introduce a new definition for nonlinear negative imaginary systems to extend the existent definition. Two different quadratic dynamic supply rates are introduced to allow for extending the dissipativity concept to cover the negative imaginary systems. One of which is a differential operator and the other is an integral operator. Both supply rates are used in order to formulate the class of negative imaginary systems as dissipative systems. This extension allows for wider class of dynamical systems to be considered in the negative imaginary framework. We also show how the new definition extends the negative imaginary system to analyze a class of higher order evolutionary dynamics. In particular, we show that the second order replicator dynamics satisfy the negative imaginary property and hence we can conclude convergence with certain class of games. Also, a nonlinear negative imaginary lemma based on the above definitions is derived.

In this article, a new soft starting control scheme based on an artificial neural network (ANN) is presented for a three-phase induction motor (IM) drive system. The main task of the control scheme is to keep the accelerating torque constant at a level based on the value of reference acceleration. This is accomplished by the proper choice of the firing angles of thyristors in the soft starter. Using the ANN approach, the complexity of the online determination of the thyristors firing angles is resolved. The IM torque-speed characteristic curves are firstly used to train the ANN model. Secondly, the IM- soft starter system is modeled using MATLAB/SIMULINK. To prove the effectiveness of the proposed ANN-based acceleration control scheme, different reference accelerations and loading conditions are applied and investigated. Finally, a laboratory prototype of 3 kW soft starter is implemented. The proposed control scheme is executed in a real-time environment using a digital signal processor (Model: TMS320F28335). The simulation and real-time results significantly confirm that the proposed controller can efficiently reduce the IM starting current and torque pulsations. This in turn ensures a smooth acceleration of the IM during the starting process. Moreover, the proposed control scheme has the superiority over several soft starting control schemes since it has a simple control circuit configuration, less required sensors, and low computational burden of the control algorithm.

Background Lung cancer is known as one of the commonest cancers globally. It is considered an important cause of mortality all over the world. Survivin, a member of the family of inhibitor of apoptosis proteins, is involved in cell division regulation and apoptosis inhibition. The survivin gene is located on the human chromosome 17q25 and consists of 142 amino acids. Cancer risk was shown to be affected by the survivin promoter −31G/C genetic polymorphism. Such genetic variance was found to be associated with aberrant survivin expression in malignant cell at both protein and mRNA levels. One of the tumor suppressor gene is the p53 protein that induces cell apoptosis. Therefore, survivin polymorphism and p53 antibodies level association was considered in non-small-cell lung cancer (NSCLC). Aim To assess survivin promoter −31G/C polymorphisms in NSCLC, with detection of p53 antibodies level and the association between it and the gene polymorphism in those patients. Patients and methods In 2019–2020, a case–control designed research work was performed at Sohag University Hospital, Egypt. A total of 60 study participants were included in our study and categorized into 15 control group and 45 histopathologically confirmed NSCLC case group. The blood samples were collected into an EDTA tube and preserved frozen till DNA extraction. Results Our study shows a highly significant variation in the prevalence of the surviving gene promoter −31G/C polymorphism between cases and control groups (P

Background Lung cancer mortality is high all over the globe. A total of three million deaths are expected to be reached in 2035. There is a rising effort nationally for cancer data documentation and networking. This study is in line with this effort. Purpose This study aimed at assessment of the survival of patients with lung cancer in the regional locality and assessing factors affecting mortality in the studied population. Patients and methods This retrospective study included patients with lung cancer who were diagnosed and received treatment in the Oncology Department, Sohag University Hospital and Sohag Oncology Institute during the period from January 2016 to June 2019. The available data in patients’ records were collected, and it included medical history, clinical finding, diagnostic and metastatic workup, treatment, and follow-up for outcome. Results A total of 160 patients were enrolled in this study. Their median survival time was 1.21 year. Nonsmall-cell lung carcinoma, squamous subtype, showed higher 3-year survival (35.67%) than other histopathological subtype. Earlier tumor stage, stage II B, showed better survival than more advanced stages. Presence of positive local signs, current smoking status, and poorly differentiated tumor were significant risk factors for mortality in final multivariate analysis. Conclusion The study documented bad prognosis of lung cancer in our regional locality. It emphasized the worse prognosis for advanced stage of tumor and confirmed the role of smoking not only in development of lung cancer but also as mortality risk factor, which highlights the importance of smoking cessation programs to be initiated with focus on public awareness about it.

The heat transfer in three-dimensional coordinates is the main focus of the present article. The cone-disk (CND) apparatus is presumed to include a stationary cone (SCN) and a rotating disk (RTD), or counter-rotating, or both of them co-rotating, along with Titanium dioxide-ethylene glycol-based nanofluid. The accommodative impact of nanopaprticles aggregation and thermal radiation is considered in the modelling equations for the flow pattern available in the literature. The modelling equations are converted into ordinary differential equations (ODEs) using similarity transformations. The behaviour of flow profiles is readily understood by employing the Runge Kutta Fehlberg fourth fifth-order (RKF45) method and the shooting approach, which is strategized and explained using graphs. The outcomes reveal that the dynamics of flow with nanoparticles aggregation case shows better-quality heat transport for increased values of radiation parameter. Furthermore, the fluid flow with aggregation shows the developed heat transfer rate at cone surface for increased values of radiation parameter.

The paper introduces a novel 3-D chaotic fractional system. A thorough analytical study of the new system is done using Lyapunov spectrum, bifurcation analysis, equilibrium point analysis, existence & uniqueness of solution, etc. The system is synchronized using a novel technique ’Quad-compound combination anti-synchronization’ with its parallel systems using non linear and adaptive sliding mode control method. A comparative study of the obtained results has been done and illustration of achieved synchronization in secure communication is also provided.

In this work, we continue our study of autonomous nonlinear dynamical systems with quaternion variables. We present a novel chaotic Chen system with quaternion variables. This system in real form is high (nine) dimensional. We study the dynamics and basic properties of this model with quaternion variables. We also evaluate the stability of the trivial points and restrict the conditions under which the nonlinear novel quaternion Chen system has negative, zero, or positive Lyapunov exponents. A signal flow graph and an electronic circuit implementation are designed, analyzed, and constructed to realize the novel Chen system. The control problem of chaotic nonlinear systems with quaternion variables is investigated. We propose and design an approach to build a controller for these systems. The viability and usefulness of the suggested approach are illustrated by an application to the chaotic Chen model with quaternion variables. Using the proposed method, the attractors of the quaternion Chen model are transformed to trivial fixed point, quasi-periodic, or periodic (limit cycle) states. The mathematical results for the controller according to this method are confirmed numerically.

In this work we display and examine the definition of complex modified (or altered) projective phase synchronization (CMPPS) of chaotic complex nonlinear frameworks which have not been presented as of late within the writing. This type of complex synchronization can be seen as a generalization in the literature of many types of synchronizations and complex synchronizations. A scheme is outlined to attain CMPPS of chaotic complex nonlinear frameworks based on the stability theory. In CMPPS, we show how nonlinear chaotic systems with complex variables can also be synchronized to a complex constant scaling matrix in a master-slave setup. The obvious change of the complex scaling matrix in CMPPS can furthermore improve the security of communications. The viability and feasibility of the CMPPS are highlighted in the recreation case.

In this work we propose the chaotic nonlinear Lü structure in quaternion form. Our new structure is high dimensional (9D). Highlights and qualities of this model are studied. Also, we present a novel king of quaternion synchronization. We call this new sort of synchronization “quaternion complete synchronization” (QCS). The idea of QCS did not consider in writing and has some unusual properties. Some organizations are conducted using the Lyapunov function to study QCS of two identical Lü attractors with quaternion variables. Numerical studies have shown the validity and accuracy of the analytical results of the control functions. Numerical studies also showed properties that distinguish QCS from the rest of the synchronization types that were previously studied.

In this paper, we discuss the idea of complex phase synchronization in complex nonlinear structures with chaotic conduct. The CPHS combines two types of common synchronizations, which are phase synchronization and anti phase synchronization. A general scheme has been proposed to study the CPHS. Through this scheme, complex control functions are assigned to obtain effective CPHS. For example, we study the CPHS in regards pair chaotic complex Lü structures including incompletely evolving for nonlinear terms. Numerical figures are drawn to prove our plan’s validity. The consequences of the CPHS are exploited in secure communications. The error function resulting from the definition of the CPHS was used as a key to retrieve the encrypted message.

The main intention of this research article is to introduce a new class of generalized fractional differential equations that fall into the categories of Sturm-Liouville’s, Langevin’s, and hybrid’s problems involving Y-Caputo fractional derivatives. The existence of the solutions of the proposed equations is discussed by using the technique of the measure of noncompactness related to the fixed point theorem, which is a generalization of Darbo’s fixed point theorem. Additionally, pertinent examples are provided along with the different values of the function Y to confirm the validity of the reported results.

In this work, we investigate the existence and uniqueness of positive solutions to a system of nonautonomous fractional differential equations. The fractional derivative of the system at hand is ψ- Riemann–Liouville fractional derivative. Some significant properties of this derivative that assist in the analysis of our results substantial are proved. The analysis is based on Guo-Krasnoselskii’s and Banach’s fixed point theorem. Finally, we give two examples to verify our results.

Whooping cough is a highly transmitted disease around the world. According to the World Health Organization (WHO), 0.15 million cases had reported globally in 2018. Most of the Asian and African states are infected regions. Through the study, we investigated the whole population into the four classes susceptible (S), exposed (E), infected (I), and vaccinated or recovered (R). The transmission dynamics of whooping cough disease are studied analytically and numerically. Analytical analyses are positivity, boundedness, reproduction number, equilibria, and local and global stabilities. In numerical analysis, we developed an implicit numerical integration scheme consistent with the biological problem’s properties. The analysis of the implicit method for the said model is dynamically consistent, positive, and bounded. Furthermore, an implicit numerical integration scheme is suitable for studying a particular epidemic model such as the whooping cough disease.

In this paper, new explicit wave solutions via liquid-gas bubbles are obtained for the fractional Kudryashov-Sinelshchikov (KS) equation under thermodynamic assumptions. A new fractional definition is applied to get these solutions that are utilized to represent the phenomenon of pressure waves under thermodynamic conditions. Two analytical techniques are used to explore the model which is sinh-Gorden equation expansion and Riccati-Bernoulli Sub-ODE methods. These approaches provide complex hyperbolic, hyperbolic, complex trigonometric, and trigonometric solutions for the fractional KS equation, particularly singular, combined singular, dark, bright, combined dark-bright, and other soliton solutions. Furthermore, acquired results are illustrated by 3D graphs for suitable parametric values that highlight the physical importance and dynamical behaviors of the equation. It is also demonstrated that the purposed approaches are powerful strategies for developing exact traveling wave solutions for a wide range of problems found in mathematical sciences.

In this work, we are concerned with some qualitative analyses of fractional-order partial hyperbolic functional differential equations under the ψ-Caputo type. To be precise, we investigate the existence and uniqueness results based on the nonlinear alternative of the Leray-Schauder type and Banach contraction mapping. Moreover, we present two similar results to nonlocal problems. Then, the guarantee of the existence of solutions is shown by Ulam-Hyer’s stability. Two examples will be given to illustrate the abstract results. Eventually, some known results in the literature are extended.

This article discusses dynamics of the fractal double-chain deoxyribonucleic acid model. This structure contains two long elastic homogeneous strands that serve as two polynucleotide chains of deoxyribonucleic acid molecules, bounded by an elastic membrane indicating hydrogen bonds between the base pairs of two chains. The semi-inverse variational principle and auxiliary equation method are employed to extricate soliton solutions. The collection of retrieved exact solutions includes bright, dark, periodic, and other solitons. The constraint conditions emerge naturally which ensure the presence of these solutions. Additionally, 2D and 3D graphs showing the impact of fractals on solutions are included. These plots use appropriate parameter values. Furthermore, sensitivity analysis of the considered model is also acknowledged. The outcomes reveal that these techniques are reliable, effective, and applicable to various biological systems.

Congestive heart failure (CHF) often leads to progressive cardiac hypertrophy and salt/water retention. However, its pathogenesis remains largely unclarified. Corin, a cardiac serine protease, is responsible for converting proANP and proBNP to biologically active peptides. Although the involvement of corin in cardiac hypertrophy and heart failure was extensively studied, the alterations in corin and proprotein convertase subtilisin/kexin-6 (PCSK6), a key enzyme in the conversion of procorin to corin, has not been studied simultaneously in the cardiac and renal tissues in cardiorenal syndrome. Thus, this study aims to examine the status of PCSK6/corin in the cardiac and renal tissues of rats with CHF induced by the creation of aorto-caval fistula (ACF). We divided rats with ACF into two subgroups based on the pattern of their urinary sodium excretion, namely, compensated and decompensated. Placement of ACF led to cardiac hypertrophy, pulmonary congestion, and renal dysfunction, which were more profound in the decompensated subgroup. Corin immunoreactive peptides were detected in all heart chambers at the myocyte membranal and cytosolic localization and in the renal tissue, especially in the apical membrane of the proximal tubule, mTAL, and the collecting duct. Interestingly, the expression and abundance of corin in both the cardiac ventricles and renal tissues were significantly increased in compensated animals as compared with the decompensated state. Noteworthy, the abundance of PCSK6 in these tissues followed a similar pattern as corin. In contrast, furin expression was upregulated in the cardiac and renal tissues in correlation with CHF severity. We hypothesize that the obtained upregulation of cardiac and renal PCSK6/corin in rats with compensated CHF may represent a compensatory response aiming at maintaining normal Na+ balance, whereas the decline in these two enzymes may contribute to the pathogenesis of avid sodium retention, cardiac hypertrophy, and blunted atrial natriuretic peptide/brain natriuretic peptide actions in decompensated CHF.

In this paper, we show a novel sort of complex synchronization. We call this sort complex modified projective lag synchronization (CMPLS). CMPLS, which is a broader instance of synchronizations, is hardly studied or not mentioned till date. We study it to a framework, with certain or uncertain parameters, of two chaotic complexes n-dimensional owing to chaotic attractors with similar structure direct parts yet differing absolutely or mostly in nonlinear terms. In view of the Lyapunov work with lag in time an approach plans are intended to accomplish CMPLS for such matches of complex frameworks with certain or indeterminate parameters. Logical expressions for the complex control capacity are determined to utilize these plans to accomplish CMPLS. This kind of complex synchronization is considered as a speculation of many sorts of synchronizations and complex synchronizations that have shown up in the current writing. The frameworks in CMPLS can be synchronized using an unpredictable scale diagonal lattice. The viability of the obtained results is represented by concentrating two cases of such coupled chaotic attractors with certain or indeterminate parameters in the complex domain. We can plot the numerical results to clear errors frameworks, modulus errors and phase errors of chaotic attractors and that can be after synchronization to show that CMPLS is accomplished. Keywords: Complex modified projective lag synchronization, Chaotic, Lyapunov function, Certain and uncertain parameters, Complex

Self-inserted urethral foreign bodies (FBs) are rare. Neither reported case was the self-inflicted FB due to a lack of financial resources nor was either case complicated by Fournier's gangrene. We present a 54-year-old male who inserted a household pipe to relieve his urine retention. Unfortunately, the FB became stuck inside, perforated the urethra, and required perineal exploration. After it was removed, the urethra was closed over a 16F urethral catheter. The wound was complicated by severe infection and resulting Fournier's gangrene. This required an additional surgery for debridement and urine diversion. Retrospectively, it would have been better if the urethra had been left open with SP tube only. We are sharing a clinical lesson learned by the practicing urologist and surgeons. Conclusively, self-inserted FBs in the urethra may lead to a series of complications. Patients with limited financial resources need more attention and care because they may hurt themselves unintentionally.

The inhibiting behavior of aluminum by the Bassia muricata extract was examined in 1.0 M H2SO4 solution as a green corrosion inhibitor via weight loss, potentiodynamic polarization (PP), electrochemical impedance spectroscopy (EIS) and electrochemical frequency modulation (EFM) techniques. It was found that the addition of the extract reduces the corrosion rate of aluminum alloy. The inhibition efficiency increases with increasing extract concentration and reached 90% at 300 ppm. The inhibitive effect of the tested extract was discussed in view of adsorption of its components on the aluminum surface. The effect of the temperature on the corrosion behavior with the addition of different concentration of B. muricata extract was studied in the temperature range of 298 and 318 K. The B. muricata extract adsorption isotherm on the aluminum surface was followed the Temkin adsorption model. The activation and adsorption parameters were computed and discussed. Tafel plots showed that the B. muricata extract represented as a mixed type inhibitor. The surface morphology was examined via scanning electron microscopy (SEM) and atomic force microscopy (AFM) which confirmed the existence of a protective film of inhibitor molecule on the aluminum surface. The results revealed that the B. muricata extract was an effective inhibitor, and the inhibition efficiencies gained from all applied techniques were in good agreement.

Introduction: Evaluation of the effectiveness of a well-targeted educational campaign specially designed toward the improvement of oral health and maintenance of removable orthodontic appliances should be considered during an orthodontic treatment. Objectives: The objective of this study was to assess the impact of the oral hygiene protocol on oral health through assessing plaque accumulation on the removable orthodontic appliance, to establish the impact of oral hygiene protocol on oral health through assessing the patients' plaque accumulation on the tooth surface and gingival bleeding, and to evaluate the degree of halitosis between the intervention and control groups. Materials and Methods: The study involved 80 patients who were equally assigned to the intervention and control removable orthodontic treatment groups. Data were collected by means of questionnaires, soft-tissue examination, breath checker, and staining the appliance with methylene blue disclosing solution. Results: The plaque score of both groups at Review 2 emphasized a significant difference (P = 0.021), yet neither differences at baseline (P = 0.989) nor Review 1 (P = 0.786) were found. The odor score of both groups at Review 2 showed a significant difference (P = 0.012). All interventional patients and only 10% of the control group patients were aware of appliance removal during sport. There was no significant difference (P = 0.211) between the responses of patients concerning the cleaning method of the appliance. The patients showed a higher user rate of mouthwash, and they were more successful with respect to when it should be used. Conclusion: The effectiveness of an educational session has been demonstrated in some aspects of the research.

Evolutionary approaches have a critical role in different disciplines such as real-world problems, computer programming, machine learning, biological sciences, and many more. The design of the stochastic model is based on transition probabilities and non-parametric techniques. Positivity, boundedness, and equilibria are investigated in deterministic and stochastic senses. An essential tool, Euler–Maruyama, is studied for the solution of said model. Standard and nonstandard evolutionary approaches are presented for the stochastic model in terms of efficiency and low-cost approximations. The standard evolutionary procedures like stochastic Euler–Maruyama and stochastic Runge–Kutta fail to restore the essential features of biological problems. On the other hand, the proposed method is efficient, of meager cost, and adopts all the desired feasible properties. At the end of this paper the comparison section is presented to support efficient analysis.

In this paper, numerical solution of third order integro-differential equation with boundary conditions is given utilizing Haar collocation technique. Both nonlinear and linear integro-differential equations are solved using this method. The third order derivative is approximated using Haar functions in both nonlinear and linear integro-differential equations. Integration is used to obtain the expression of lower order derivatives as well as the solution for the unknown function. The Gauss elimination approach is utilized for linear systems and Broyden approach is adopted for nonlinear systems. Validation and convergence of the proposed approach are illustrated using some examples. At various collocation and gauss points, the maximum absolute and root mean square errors are compared to the exact solution. The convergence rate is also measured using different numbers of nodal points, and it is nearly equal to 2.

In this article, a new and efficient operational matrix method based on the amalgamation of Fibonacci wavelets and block pulse functions is proposed for the solutions of time-fractional telegraph equations with Dirichlet boundary conditions. The Fibonacci polynomials and the corresponding wavelets along with their fundamental properties are briefly studied at first. These functions along with their nice characteristics are then utilized to formulate the Fibonacci wavelet operational matrices of fractional integrals. The proposed method reduces the fractional model into a system of algebraic equations, which can be solved using the classical Newton iteration method. Approximate solutions of the time-fractional telegraph equation are compared with the recently appeared Legendre and Sinc-Legendre wavelet collocation methods. The numerical outcomes show that the Fibonacci technique yields precise outcomes and is computationally more effective than the current ones.

The article introduces the fractional modified Sprott A chaotic system with its thorough dynamical analysis such as solution of system, Lyapunov dynamics, route to chaos etc. Penta-compound combination anti-synchronization is introduced and applied on twelve chaotic systems of fractional order using adaptive SMC. The system is also controlled about a randomly chosen point and The synchronization technique is illustrated as application to secure communication. The simulations are performed using MATLAB software.

In this paper we consider ant-eating pangolin as a possible source of the novel corona virus (COVID-19) and propose a new mathematical model describing the dynamics of COVID-19 pandemic. Our new model is based on the hypotheses that the pangolin and human populations are divided into measurable partitions and also incorporates pangolin bootleg market or reservoir. First we study the important mathematical properties like existence, boundedness and positivity of solution of the proposed model. After finding the threshold quantity for the underlying model, the possible stationary states are explored. We exploit linearization as well as Lyapanuv function theory to exhibit local stability analysis of the model in terms of the threshold quantity. We then discuss the global stability analyses of the newly introduced model and found conditions for its stability in terms of the basic reproduction number. It is also shown that for certain values of R0, our model exhibits a backward bifurcation. Numerical simulations are performed to verify and support our analytical findings.

This manuscript investigates the accuracy of the solitary wave solutions of the (2+1)-dimensional nonlinear Chiral Schrödinger ((2+1)-D CNLS) equation that are constructed by employing two recent analytical techniques (modified Khater (MKhat) and modified Jacobian expansion (MJE) methods). This investigation is based on evaluating the initial and boundary conditions through the obtained analytical solutions then employing the Adomian decomposition (AD) method to evaluate the approximate solutions of the (2+1)-D CNLS equation. This framework gives the ability to get large complex traveling wave solutions of the considered model and shows the superiority of the employed computational schemes by comparing the absolute error for each of them. The handled model describes the edge states of the fractional quantum hall effect. Many novel solutions are obtained with various formulas such as trigonometric, rational, and hyperbolic to the studied model. For more illustration of the results, some solutions are displayed in 2D, 3D, and density plots.

Without four-wave mixing terms in birefringent fibers, the extended trial function scheme was used to obtain optical soliton solutions for the coupled system corresponding to the Gerdjikov-Ivanov equation. The procedure reveals singular soliton solutions, bright soliton solutions, and highly important solutions in terms of Jacobi’s elliptic function. And in the limiting case of the modulus of ellipticity, singular and singular-periodic soliton solutions, along with their respective existence criteria.

In this work, we exemplify the behaviour of the nonlinear model of arbitrary order differential equations by adopting q-homotopy analysis transform method (q-HATM). In the present study, the illustrated scheme is a graceful amalgamation of Laplace transform with q-homotopy analysis algorithm and we considered arbitrary order derivative using Atangana-Baleanu (AB) operator. The suggested nonlinear system exhibits chaotic behaviour in nature with respect to considered initial conditions. Fixed point hypothesis heard present the existence and uniqueness for the attained solution. We exemplified suggested arbitrary order system with to illustrate and confirm the efficiency of the projected solution procedure. Further, the numerical simulation is illustrated and also the chaotic behaviour of the obtained result captured with respect to arbitrary order in terms of plots. The obtained results confirm the projected scheme is highly methodical, easy to implement and very powerful to exemplify the nature of the dynamical system of arbitrary order.

The worldwide association of health (WHO) has stated that COVID-19 (the novel coronavirus disease-2019) as a pandemic. Here, the common SEIR model is generalized in order to show the dynamics of COVID-19 transmission taking into account the ABO blood group of the infected people. Fractional order Caputo derivative are used in the proposed model. Our study is guided by the results that have been obtained by Chen J, Fan H, Zhang L, et al. from three unique medical clinics in Wuhan and Shenzhen, China. In this study, the feasibility region of the proposed model are calculated plus the points of equilibrium. Also, the equilibrium points stability is examined. A unique solution existence for the proposed paradigm is proved via utilizing the fixed point theory with regards to Caputo fractional derivative. Numerical experiments of the proposed paradigm is done and we show its sensitivity to the fractional order.

It is of great curiosity to observe the effects of prevention methods and the magnitudes of the outbreak including epidemic prediction, at the onset of an epidemic. To deal with COVID-19 Pandemic, an SEIQR model has been designed. Analytical study of the model consists of the calculation of the basic reproduction number and the constant level of disease absent and disease present equilibrium. The model also explores number of cases and the predicted outcomes are in line with the cases registered. By parameters calibration, new cases in Pakistan are also predicted. The number of patients at the current level and the permanent level of COVID-19 cases are also calculated analytically and through simulations. The future situation has also been discussed, which could happen if precautionary restrictions are adopted.

The present paper is concerned with the implementation of the optimal homotopy asymptotic method to find the approximate solutions of two-dimensional fractional order Volterra integro-differential equations. The technique’s applicability and validity are tested through some numerical examples. The fractional order derivatives are calculated using Caputo’s sense. Results obtained by the proposed technique are compared with the Legendre wavelet method. The proposed method provides us with efficient and more accurate solutions than the other existing methods in the literature. Error analysis and convergence of the proposed method are also provided in the paper.

In the manuscript, fractional order neural network under electromagnetic radiation is introduced and its dynamics studied using Lyapunov exponents, stagnation points, symmetry, bifurcation diagrams etc. The dynamics for variable fractional order between 0.8 to 1 is also observed. The neural network model shows high sensitivity to external stimuli. The neural functioning shows improvement when exposed to the right amount of electromagnetic radiations. The chaos in the studied dynamical system is controlled about its unique stagnation point using SMC controllers in presence of uncertainties and disturbances, which are also estimated in this method. These results could bring vision into the occurrence of neuron related problems.

In this work, the nonlinear Schrödinger’s equation is studied for birefringent fibers incorporating four-wave mixing. The improved tanϕ(ξ)2-expansion, first integral, and G′G2-expansion methods are used to extract a novel class of optical solitons in the quadratic-cubic nonlinear medium. The extracted solutions are dark, periodic, singular, and dark-singular, along with other soliton solutions. These solutions are listed with their respective existence criteria. The recommended computational methods here are uncomplicated, outspoken, and consistent and minimize the computational work size, which give it a wide range of applicability. A detailed comparison with the results that already exist is also presented.

In the work, author’s presents a very significant and important issues related to the health of mankind’s. Which is extremely important to realize the complex dynamic of inflected disease. With the help of Caputo fractional derivative, We capture the epidemiological system for the transmission of Novel Coronavirus-19 Infectious Disease (nCOVID-19). We constructed the model in four compartments susceptible, exposed, infected and recovered. We obtained the conditions for existence and Ulam’s type stability for proposed system by using the tools of non-linear analysis. The author’s thoroughly discussed the local and global asymptotical stabilities of underling model upon the disease free, endemic equilibrium and reproductive number. We used the techniques of Laplace Adomian decomposition method for the approximate solution of consider system. Furthermore, author’s interpret the dynamics of proposed system graphically via Mathematica, from which we observed that disease can be either controlled to a large extent or eliminate, if transmission rate is reduced and increase the rate of treatment.

In the manuscript fractional tumour growth and decay model is studied extensively using various dynamic analysis methods such as Lyapunov exponents, bifurcation and fixed point analysis, solution and so on. The model dynamics is observed by changing order between 0.8 and 1. Chaos has been observed in this fractional tumour growth and decay model. The model is also stabilized about its equilibrium points by chaos control technique using adaptive sliding mode control scheme. Numerical simulations are carried out to validate the theoretical results. These observations may prove fruitful and provide insight to deal with the disease.

Na+/H+ exchangers (NHEs), encoded by Solute Carrier 9A (SLC9A) genes in human, are ubiquitous integral membrane ion transporters that mediate the electroneutral exchange of H+ with Na+ or K+. NHEs, found in the kidney and intestine, play a major role in the process of fluid reabsorption together via Na+,K+-ATPase pump and Na+ channels. Nevertheless, the expression pattern of NHE in the lung and its role in alveolar fluid homeostasis has not been addressed. Therefore, we aimed to examine the expression of NHE specific isoforms in alveolar epithelial cells (AECs), and assess their role in congestive heart failure (CHF). Three NHE isoforms were identified in AEC and A549 cell line, at the level of protein and mRNA; NHE1, NHE2 and mainly NHE8, the latter was shown to be localized in the apical membrane of AEC. Treating A549 cells with angiotensin (Ang) II for 3, 5 and 24 hours displayed a significant reduction in NHE8 protein abundance. Moreover, the abundance of NHE8 protein was downregulated in A549 cells that were treated overnight with Ang II. NHE8 abundance in whole lung lysate was increased in rats with 1-week CHF compared to sham operated rats. However, lower abundance of NHE8 was observed in 4-week CHF group. In conclusion, we herein show for the first time, the expression of a novel NHE isoform in AEC, namely NHE8. Notably, Ang II decreased NHE8 protein levels. Moreover, NHE8 was distinctly affected in CHF rats, probably depending on the severity of the heart failure.

The aim of this investigation is making mathematical model for the variation in laser pulse, rotational gravity, and magnetic fields on the generalized thermoelastic homogeneous isotropic half-space. The governing dynamical system equations have been formulated considering the four thermoelastic models: coupled (CT) model, Lord and Shulman (LS) model, Green and Lindsay (GL) theory, and Green and Naghdi (GN III) model. Normal mode analysis technique is used to obtain the analytical expressions for the displacement components, temperature, and mechanical and Maxwell’s stresses distribution. The effect of laser pulse, gravity, and magnetic field is studied by numerical examples and displayed graphically. A comparison has been made between the theories as well as the present results and agreement with it as a special case from this study. The results predict the strong effect of magnetic field, laser pulse, and gravity field on the wave propagation phenomenon.

We present a new viable nonlinear chaotic paradigm. This paradigm has four nonlinear terms. The essential features of the new paradigm have been investigated. Our new system is confirmed to have chaotic behaviors by calculating its Lyapunov exponents. The relations of the system states are displayed by a suggested new signal flow graph (SFG). The proposed SFG is discussed via some graph theory tools, and some of its hidden features are calculated. In addition, the system is realized via constructing its electronic circuit which helps in the real applications. Also, a robust controller for the system is designed with the aid of a genetic algorithm.

The main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation rlu′lγ′+qlxβσl=0, where l≥l0 and ul≔xl+pxϱl. By optimizing the commonly used relationship x>1−pu, we obtain new criteria that give sharper results for oscillation than the previous related results. Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.

This article examines a natural convection viscous unsteady fluid flowing on an oscillating infinite inclined plate. The Newtonian heating effect, slip effect on the boundary wall, and constant mass diffusion conditions are also considered. In order to account for extended memory effects, the semi-analytical solution of transformed governed partial differential equations is attained with the help of a recent and more efficient fractional definition known as Prabhakar, like a thermal fractional derivative with Mittag-Leffler function. Fourier and Fick’s laws are also considered in the thermal profile and concentration field solution. The essentials’ preliminaries, fractional model, and execution approach are expansively addressed. The physical impacts of different parameters on all governed equations are plotted and compared graphically. Additionally, the heat transfer rate, mass diffusion rate, and skin friction are examined with different numerical techniques. Consequently, it is noted that the variation in fractional parameters results in decaying behavior for both thermal and momentum profiles while increasing with the passage of time. Furthermore, in comparing both numerical schemes and existing literature, the overlapping of both curves validates the attained solution of all governed equations.

To improve the structural stiffness, strength and reduce the weight of nanoplate structure, functionally graded (FG) graphene-reinforced nanocomposite (GRNC) laminated plates are exploited in this paper. The bending and buckling behaviors of FG-GRNC laminated nanoplates are investigated by using novel quasi-3D hyperbolic higher order shear deformation plate theory in conjunction with modified continuum nonlocal strain gradient theory, which considered both length and material scale parameters. The modified model of Halpin–Tsai is employed to calculate the effective Young’s modulus of the GRNC plate along the thickness direction, and Poisson’s ratio and mass density are computed by using the rule of mixture. An analytical approach of the Galerkin method is developed to solve governing equilibrium equations of the GRNC nanoplate and obtain closed-form solutions for bending deflection, stress distributions and critical buckling loads. A detailed parametric analysis is carried out to highlight influences of length scale parameter (nonlocal), material scale parameter (gradient), distribution pattern, the GPL weight fraction, thickness stretching, geometry and size of GPLs, geometry of the plate and the total number of layers on the stresses, deformation and critical buckling loads. Some details are studied exclusively for the first time, such as stresses and nonlocality effect.

Applying several latest theoretical techniques, the empirical description of the interaction between the high-frequency Langmuir and the low-frequent ion-acoustic waves, derived mathematically by Zakharov’s non-dimensional (ZE) equation. These interactions are described in electromagnetic waves, plasma physics, signal processing through optical fibers, coastal engineering, and fluid dynamics. Three modern computing methods are being used to construct several solutions: the extended exp(ϕ)-expansion process,the popular Kudryashov process, and the modified Khather method. Centered on the properties of the Hamilton system, the stability properties of the solutions are investigated. The physical proprieties are illustrated using 3D plots. The originality of the obtained solutions is explored. We demonstrate that we retrieve the old known solutions and we obtain new solutions that have never been found before.

This study is aimed at developing new criteria of the iterative nature to test the oscillation of neutral delay differential equations of third order. First, we obtain a new criterion for the nonexistence of the so-called Kneser solutions, using an iterative technique. Further, we use several methods to obtain different criteria, so that a larger area of the models can be covered. The examples provided strongly support the importance of the new results.

In this paper, a generalized algorithm to develop a class of approximating binary subdivision schemes is presented. The proposed algorithm is based on three-point approximating binary and four-point interpolating binary subdivision schemes. It contains a parameter which classifies members of the new class of subdivision schemes. A set of efficient properties, for instance, polynomial generation and reproduction, support, continuity, and Hölder continuity, is discussed. Moreover, applications of the proposed subdivision schemes are given in order to demonstrate their variety, flexibility, and visual performance.