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Automated segmentation of diseases considered a necessary initial step in routine diagnosis. Lung diseases that affect the lungs, such as pneumonia or lung collapse can result in areas of consolidation or atelectasis, where lung tissue becomes denser or collapses. It can be challenging to accurately segment such areas, as they may exhibit similar characteristics to adjacent structures. This study proposes a lung CT image segmentation method which includes two steps: (1) a new image enhancement model that uses the bounded turning Mittag-Leffler function to improve the CT images for better segmentation outcomes. (2) a new modified VGG-16 for infection of lung segmentation based on expanding the original VGG-16 network. The dilated convolutional layers are added to the original VGG-16 network to create a new lung CT image segmentation method. The experimental results showed that the proposed method can accurately segment the infected region in lung CT scans. The results led to Accuracy, Dice Coefficient and Jaccard Index values of 96.3%, 91.2%, and 82.3% respectively. The proposed method is accurate and suitable for implementation in real-world applications. Following result computation, seven related studies are compared with the recommended methodology. This demonstrated how well this study had performed in comparison to many earlier studies. Despite the fact that segmenting lung CT images requires a lot of work. Obtaining a suitable level of accuracy was quite difficult.

In this note, we suggest a generalization of gamma function to be 3D-gamma function. As a consequence, some special functions are generalized including the Mittag–Leffler function. Moreover, we utilize the generalized Mittag–Leffler to extend the AB-fractional calculus. Examples are introduced to cover our theory. The solvability of abstract Riccati equation is considered, and Hyers–Ulam stability is discovered in the sequel. Based on the new study, we design new stable of Self-organization in complex networks (SOCNs).

Plant diseases can spread rapidly, leading to significant crop losses if not detected early. By accurately identifying diseased plants, farmers can target treatment only to the affected areas, reducing the number of pesticides or fungicides needed and minimizing environmental impact. Tomatoes are among the most significant and extensively consumed crops worldwide. The main factor affecting crop yield quantity and quality is leaf disease. Various diseases can affect tomato production, impacting both yield and quality. Automated classification of leaf images allows for the early identification of diseased plants, enabling prompt intervention and control measures. Many creative approaches to diagnosing and categorizing specific illnesses have been widely employed. The manual method is costly and labor-intensive. Without the assistance of an agricultural specialist, disease detection can be facilitated by image processing combined with machine learning algorithms. In this study, the diseases in tomato leaves will be detected using new feature extraction method using conformable polynomials image features for accurate solution and faster detection of plant diseases through a machine learning model. The methodology of this study based on: • Preprocessing, feature extraction, dimension reduction and classification modules. • Conformable polynomials method is used to extract the texture features which is passed classifier. • The proposed texture feature is constructed by two parts the enhanced based term, and the texture detail part for textual analysis. • The tomato leaf samples from the plant village image dataset were used to gather the data for this model. The disease detected are 98.80 % accurate for tomato leaf images using SVM classifier. In addition to lowering financial loss, the suggested feature extraction method can help manage plant diseases effectively, improving crop yield and food security.

By using the generalization of the gamma function (p-gamma function: Γp(.)), we introduce a generalization of the fractal–fractional calculus which is called p-fractal fractional calculus. We extend the proposed operators into the symmetric complex domain, specifically the open unit disk. Normalization for each operator is formulated. This allows us to explore the most important geometric properties. Examples are illustrated including the basic power functions.

In this effort, we present a new definition of the Steiner symmetrization by using special analytic functions in a complex domain (the open unit disk) with respect to the origin. This definition will be used to optimize the class of univalent analytic functions. Our method is based on the concept of differential subordination and the Carathéodory theory. Examples are illustrated in the sequel involving the modified Libera–Livingston–Bernardi integral operator over the open unit disk. The result gives that this integral satisfies the definition of bounded turning function (univalent analytic function).

Mathematics has several uses for operators on bounded symmetric domains of Bergman spaces including complex geometry, functional analysis, harmonic analysis and operator theory. They offer instruments for examining the interaction between complex function theory and the underlying domain geometry. Here, we extend the Atangana-Baleanu fractional differential operator acting on a special type of class of analytic functions with the m-fold symmetry characteristic in a bounded symmetric domain (we suggest the open unit disk). We explore the most significant geometric properties, including convexity and star-likeness. The boundedness in the weighted Bergman and the convex Bergman spaces associated with a bounded symmetric domain is investigated. A dual relations exist in these spaces. The subordination and superordination inequalities are presented. Our method is based on Young's convolution inequality.

A fractal–fractional calculus is presented in term of a generalized gamma function (ℓ−gamma function: Γℓ(.)). The suggested operators are given in the symmetric complex domain (the open unit disk). A novel arrangement of the operators shows the normalization associated with every operator. We investigate a number of significant geometric features thanks to this. Additionally, some integrals, such the Alexander and Libra integral operators, are associated with these operators. Simple power functions are among the illustrations that are provided. Additionally, the formulation of the discrete ℓ−fractal–fractional operators is conducted. We demonstrate that well-known examples are involved in the extended operators.

Numerous special functions, including the beta function, hypergeometric functions, and other orthogonal polynomials, are closely connected to the gamma function. Recently, gamma function has been enhanced by adding a new parameter. As a consequence, this gamma is called the parametric gamma function or b-gamma function. By utilizing the enhanced gamma function (or the parametric gamma function), we have present a generalization for the special function Rabotnov function. Consequently, new fractal-fractional operators (derivative and integral) involving the generalized Rabotnov function are defined. Analysis is introduced to discover the main properties of the suggested operators. Since the main challenge in the calculus of fractal-fractional operators is to design examples, we illustrate a set of examples including power series. We explore the boundedness of the recommended operators. There are many gains for checking the boundedness of fractal operators in general and fractal-fractional operators in particular. Moreover, as an application, we establish the existence and uniqueness solution of abstract fractal-fractional equation. Examples are presented at the end of the effort. Graphics and computations are observed using MATHEMATICA 13.3 software. • By using the parametric gamma function, the Rabotnov special function is generalized. New fractal-fractional operators are presented using the generalized Rabotnov function with examples; • Boundedness of these operators is investigated, where bounded operators give a strong foundation for understanding linear transformations across normed spaces, with many applications in science and mathematics. • Conditions of the existence and uniqueness of solutions of fractal-fractional differential abstract equation are established.

Abstract Medical imaging is considered a suitable alternative testing method for the detection of lung diseases. Many researchers have been working to develop various detection methods that have aided in the prevention of lung diseases. To better understand the condition of the lung disease infection, chest X-Ray and CT scans are utilized to check the disease’s spread throughout the lungs. This study proposes an automated system for the detection multi lung diseases in X-Ray and CT scans. A customized convolutional neural network (CNN) and two pre-trained deep learning models with a new image enhancement model are proposed for image classification. The proposed lung disease detection comprises two main steps: pre-processing, and deep learning classification. The new image enhancement algorithm is developed in the pre-processing step using k-symbol Lerch transcendent functions model which enhancement images based on image pixel probability. While, in the classification step, the customized CNN architecture and two pre-trained CNN models Alex Net, and VGG16Net are developed. The proposed approach was tested on publicly available image datasets (CT, and X-Ray image dataset), and the results showed classification accuracy, sensitivity, and specificity of 98.60%, 98.40%, and 98.50% for the X-Ray image dataset, respectively, and 98.80%, 98.50%, 98.40% for the CT scans dataset, respectively. Overall, the obtained results highlight the advantages of the image enhancement model as a first step in processing.

By using the most generalized gamma function (parametric gamma function, or p-gamma function), we present the most generalized Rabotnov function, called the p-Rabotnov function. Consequently, new fractal–fractional differential and integral operators of a complex variable in an open unit disk are defined and investigated analytically and geometrically. We address some inequalities involving the generalized fractal–fractional integral operator in some spaces of analytic functions. A novel complex fractal–fractional integral transform (CFFIT) is presented. A normalization of the proposed CFFIT is observed in the open unit disk. Examples are illustrated for power series of analytic functions.

The goal is to take advantage of the Earth-ionosphere wave guide’s fundamentally two-dimensional wave propagation, utilizing the normalized Airy functions (NAFs) in a complex domain. It is demonstrated that the typical working formula of VLF radio-mode theory may be obtained simply from orthogonality reflections, devoid of the requirement of sophisticated argumentation in the open unit disk. The combination of the expressions is given by considering the symmetry-convex illustration of the NAFs.

It has been shown that the findings of d-metric spaces may be deduced from S-metric spaces by considering dϖ,ϰ=Λϖ,ϖ,ϰ. In this study, no such concepts that translate to the outcomes of metric spaces are considered. We establish standard fixed point theorems for integral type contractions involving rational terms in the context of complete S-metric spaces and discuss their implications. We also provide examples to illustrate the work. This paper’s findings generalize and expand a number of previously published conclusions. In addition, the abstract conclusions are supported by an application of the Riemann-Liouville calculus to a fractional integral problem and a supportive numerical example.

The current research looks into magnetohydrodynamics Casson nanofluid flow and suction/injection implications for a nonlinearly stretched interface. To improve heat transport, joules of heat, radiation impacts and thermal stratification are used. A Darcy-Forchheimer porous media is used to conduct fluid flow. Chemical reactions involving energies of activation and solutal stratum are additionally considered. The Keller-box technique is used to solve the resulting non-linear set of ordinary differential equations. The impacts of a number of variables are examined employing diagrams of quantity, velocity, and heat. Increased assessments of porousness, Darcy-Forchheimer, and Casson fluid characteristics result in a decrease in velocity trends. For improved measurements of Lewis number and solutal fractionated factors, the intensity pattern reduces. The skin friction factor increases with increasing Casson parameter estimate. In the instance of the porous and nonlinear stretching parameters, the Nusselt number rises. For increasing levels of the Lewis number and Brownian motion factors, the Sherwood number drops. Furthermore, Nusselt number ratios are estimated with Prandtl numbers with regard to current information available, which shows remarkable consistency. For varied incorporated parameters, streamlines, heatlines, and masslines additionally displayed.

The type of symmetry exhibited by a travelling wave can have important implications for its behaviour and properties, such as its polarization, dispersion, and interactions with other waves or boundaries. The fractional differential Duffing problem refers to the mathematical modelling of nonlinear, damped oscillations of a system with fractional derivatives. It is a generalization of the classical Duffing equation, which describes the behaviour of a nonlinear, damped oscillator (the equation becomes symmetric under time-reversal). The fractional derivatives allow for a more accurate description of the system's memory and hereditary properties. The solution of the fractional Duffing equation can provide insight into the complex dynamic behaviour of various physical, biological, and engineering systems. We are concerned with studying a new differential Duffing fractional problem. It involves some sequential Caputo derivatives with an infinite series of Riemann–Liouville integrals and some other functions. We begin by proving a first existence and uniqueness result, then we discuss two types of stability for the obtained uniqueness result. An illustrative examples is given to show the applicability of the result. We are also concerned with applying the Tanh method to obtain new classes of travelling wave solutions for three important classes of (Khalil) fractional conformable problems; the generalized equation of Duffing, the Landau–Ginzburg–Higgs equation and the Sine–Gordon one. Some numerical simulations are plotted and a conclusion is given at the end.

Artificial neural networks (ANNs) have a wide range of applications in science and technology. Artificial neural networks (ANNs) widely utilized in image and speech recognition, neural language processing, drug discovery, genomics and bioinformatics, Robotics and control systems, material science and energy and power system. Due to the above applications, the main focus of this article is to scrutinize the impact of inclined magnetic field on a cross nanofluid flow with slip velocity and convective boundary conditions over a variable porosity. Gold (Au) nanoparticles are suspended in base liquid blood. Thermal stratification and heat generation with joule heating impact is taken in the energy equation in order to see the heat transfer. To transform the non-linear partial differential equations (PDE's) into non-linear ordinary differential equations (ODE's) utilized the von-Karman similarity transformation parameters. For the solutions of the non-linear ODE's, the 4th- order Runge-Kutta numerical method is employed. A dataset for the employed neural network back propagated Levenberg-Marquard scheme (NN-BLMS) is generated for various estimations of the embedded parameters like Weissenberg number, magnetic parameter, angle of inclination, porosity and permeability parameters, thermal stratification parameter by utilizing the 4th-order Runge-Kutta numerical scheme. The testing, validation and training methods of NN-BLMS are utilized to scrutinize the approximate solution of cross nanofluid with slip velocity and convective boundary conditions. The performance of the proposed NN-BLMS to successfully solved the cross nanofluid model is endorsed via mean squared error, error histogram and regression analysis. Streamlines and heatlines are plotted for different parameters including in velocity and temperature equations.

Analytic functions are very helpful in many mathematical and scientific uses, such as complex integration, potential theory, and fluid dynamics, due to their geometric features. Particularly conformal mappings are widely used in physics and engineering because they make it possible to convert complex physical issues into simpler ones with simpler answers. We investigate a novel family of analytic functions in the open unit disk using the K-symbol fractional differential operator type Riemann-Liouville fractional calculus of a complex variable. For the analysis and solution of differential equations containing many fractional orders, it offers a potent mathematical framework. There are ongoing determinations to strengthen the mathematical underpinnings of K-symbol fractional calculus theory and investigate its applications in various fields. • Normalization is presented for the K-symbol fractional differential operator. Geometric properties are offered of the proposed K-symbol fractional differential operator, such as the starlikeness property and hence univalency in the open unit disk. • The formula of the Alexander integral involving the proposed operator is suggested and studied its geometric properties such as convexity. • Examples are illustrated to fit our pure result. Here, the technique is based on the concepts of geometric function theory in the open unit disk, such as the subordination and Jack lemma.

Many image-processing applications heavily depend on the quality of medical images. Due to the unpredictable variation in the captured images, medical images frequently have problems with noise or low contrast; therefore, improving medical imaging is a challenging task. For better treatment, physicians need images with good contrast to provide the most detailed picture of the disease. The generalized k-differential equation based on the k-Caputo fractional differential operator (K-CFDO) is used in this study to determine the energy of the image pixels to improve the visual quality and provide a clearly defined problem. The logic behind using the K-CFDO approach in image enhancement is the ability of K-CFDO to efficiently capture high-frequency details using the probability of pixels as well as preserve the fine image details. Moreover, the visual quality of X-ray images is improved by performing a low-contrast X-ray image enhancement. • Determine the energy of the image pixels for better pixel intensity enhancement. • Capture high frequency image details using the image probability of pixels.The findings of this study indicate that the average Brisque, Niqe, and Piqe values for the provided chest X-ray were found to be (Brisque=23.25, Niqe=2.8, Piqe21.58), and for the dental X-ray, they were (Brisque=21.12, Niqe=3.77, Piqe=23.49). The results of this study show potential improvements with the proposed enhancement methods that may contribute to increasing efficiency in healthcare processes at rural clinics. Generally, this model improves the details of medical images, which may aid medical staff throughout the diagnostic process by increasing the efficiency and accuracy of clinical decisions. Due to the improper setting of the suggested enhancing parameters, the current study included a limitation on image over-enhancement.

As a result of its use in the manufacturing and construction industries, research on the flow of nanofluid is rather well-known among academics and professionals in related fields. It is helpful for electrical equipment to utilize it for cooling reasons, which has shown promising results in terms of reducing energy use. As a result, the primary objective of this research is to inspect the impacts that radiation has on the mixed convection of Walters'-B hybridity nanofluid flow of stagnant point in a horizontal circular cylinder under the circumstances of a constant heat flux. It is considered a conventional fluid despite the presence of copper (Cu) and alumina (Al2O3) nanoparticles in the water (H2O) hybridity nanofluid. To make the solution to the resulting controlling system of equations more straightforward, the numerical approach of a neural network with a back-propagation algorithm (NN-BPA) is used. It follows by clarifying how various physical characteristics, such as blended convection, thermal radiation, and stagnant movement, affect temperature, skin friction, thermal transfer, velocity, and graphical profiles of those variables. The LMNN-BPA has the quickest processing algorithm and performs well in general, corresponding to the thorough analysis. Additionally, the mixed convective and viscoelastic properties exhibit both rising and dropping developments regarding skin friction and heat transmission.

In this work was prepared α-Al2O3 alloys from laboratory aluminum oxide powder that was milled for different periods of time and sintered at a temperature of 1450 °C. The difference between the prepared samples was studied using several experimental measurement techniques, including X-ray diffraction, scanning electron microscopy and measurement of physical and mechanical properties. Moreover, the effect of milling time on the formation and sintering of alpha-alumina, by milling the mixture at different times using high energy crushing technique was studied. An influence of milling time on density, open spaces and microstructure of the samples was analyzed. The obtained results showed that longer milling duration led to alloys with higher hardness (H) and modulus of elasticity (E). This improvement is due to lower porosity and corresponding higher density at high temperatures. A noticeable decrease in the size of the particles with the increase of the milling time led to an increase in the lattice parameter accompanied by a decrease in defects and ionic voids. The percentage of pores reached 0.04 % within 24 h of grinding after it was approximately 0.20 %, while the density reached 96 % after the same highest grinding time. Tests showed that the value of friction coefficient decreases, while it increases with the increase in the applied pressure force and this was confirmed by SEM images of the samples. the main factor to reduce friction is the increase in grinding time, regardless of the value of the applied load. The results showed that the Al2O3 alloy applied to it with a load of 2 N and milled for 24 h had a minimum value of 1.94 µm3 wear volumes and a wear rate of 1.33 (µm3∙N−1∙µm−1). The sample milled for 24 h showed the best result, characterized by the lowest wear size, specific wear rate and the highest hardness with extraordinary density of 96 %, which is important in the field of biomaterials applications.

Impulsive is the affinity to do something without thinking. In this effort, we model a mathematical formula types integro-differential equation (I-DE) to describe this behavior. We investigate periodic boundary value issues in Banach spaces for fractional a class of I-DEs with non-quick impulses. We provide numerous sufficient conditions of the existence of mild outcomes for I-DE utilizing the measure of non-compactness, the method of resolving domestic, and the fixed point result. Lastly, we illustrate a set of examples, which is given to demonstrate the investigations key findings. Our findings are generated some recent works in this direction.

Researchers across the world have tried to explore the impact of various hybrid nanoparticles in the case of fluid moving over a disk with the inclusion of various effects to investigate heat and made transfer analyses of fluid. The present article is designed to scrutinize the influence of Diathermic oil (DO) with the inclusion of tri-hybrid nanoparticles by adopting a tri-hybrid Yamada-Ota and Xue nanofluid model. The article is novel in the sense that the extension in Yamada-Ota and Xue nanofluid models in the case of tri-hybrid nanoparticles has never studied before in the existing literature. Diathermic oil (DO) is a great quality mineral oil that has been refined to assure long-term service due to its outstanding resistance to thermal cracking and chemical oxidation; also, its high specific heat and thermal conducting offer fast heat loss. Our goal in this work is to compare the concert of the Yamada-Ota and Xue representations for a nanofluid movement between two revolving disks in a spongy medium in light of these astonishing physiognomies. The entire scenario is thought out with different traits. Using the Keller box approach, the governing system's numerical solution is achieved. The feature consequences of ascending constraints solid nanoparticles capacity fraction (0.005≤ϕ=ϕ1+ϕ2+ϕ3≤0.15), heat ratio θw, fluid parameter β, porosity parameter M, temperature generating and sink having varieties A∗, and B∗, radiative parameter Rd, and Eckert number Ec between 0.1 and 2, versus connected outlines are examined. When the variable viscosity parameter (for gases) is positive, the axial velocity decreases; however, when the varying viscidness parameter is negative, the rapidity distribution increases (liquids).

Purpose – In this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory. The analytic solutions of the LDEs are considered by utilizing the Caratheodory functions joining the subordination concept. A class of Caratheodory functions involving special functions gives the upper bound solution. Design/methodology/approach – The methodology is based on the geometric function theory. Findings – The authors present a new analytic function for a class of complex LDEs. Originality/value – The authors introduced a new class of complex differential equation, presented a new technique to indicate the analytic solution and used some special functions.

The variable fractional Lozi map (VFLM) and the variable fractional flow map are two separate systems that we propose in this inquiry. We study several key dynamics of these maps. We also investigate the sufficient and necessary requirements for the stability and asymptotic stability of the variable fractional dynamic systems. As a result, we provide VFLM with the necessary criteria to produce stable and asymptotically stable zero solutions. Furthermore, we propose a combination of these maps in control rules intended to stabilize the system. In this analysis, we take the 1D- and 2D-controller laws as givens.

Abstract For heating, ventilation or air conditioning purposes in massive multistory building constructions, ducts are a common choice for air supply, return, or exhaust. Rapid population expansion, particularly in industrially concentrated areas, has given rise to a tradition of erecting high-rise buildings in which contaminated air is removed by making use of vertical ducts. For satisfying the enormous energy requirements of such structures, high voltage wires are used which are typically positioned near the ventilation ducts. This leads to a consequent motivation of studying the interaction of magnetic field (MF) around such wires with the flow in a duct, caused by vacuum pump or exhaust fan etc. Therefore, the objective of this work is to better understand how the established (thermally and hydrodynamically) movement in a perpendicular square duct interacts with the MF formed by neighboring current-carrying wires. A constant pressure gradient drives the flow under the condition of uniform heat flux across the unit axial length, with a fixed temperature on the duct periphery. After incorporating the flow assumptions and dimensionless variables, the governing equations are numerically solved by incorporating a finite volume approach. As an exclusive finding of the study, we have noted that MF caused by the wires tends to balance the flow reversal due to high Raleigh number. The MF, in this sense, acts as a balancing agent for the buoyancy effects, in the laminar flow regime

A generalized differential operator utilizing Raina's function is constructed in light of a certain type of fractional calculus. We next use the generalized operators to build a formula for analytic functions of type normalized. Our method is based on the concepts of subordination and superordination. As an application, a class of differential equations involving the suggested operator is studied. As seen, the solution is provided by a certain hypergeometric function. We also create a fractional coefficient differential operator. Its geometric and analytic features are discussed. Finally, we use the Jackson's calculus to expand the Raina's differential operator and investigate its properties in relation to geometric function theory.

Abstract The flow of a fluid across a revolving disc has several technical and industrial uses. Examples of rotating disc flows include centrifugal pumps, viscometers, rotors, fans, turbines, and spinning discs. An important technology with implications for numerous treatments utilized in numerous sectors is the use of hybrid nanofluids (HNFs) to accelerate current advancements. Through investigation of ternary nanoparticle impacts on heat transfer (HT) and liquid movement, the thermal properties of tri-HNFs were to be ascertained in this study. Hall current, thermal radiation, and heat dissipation have all been studied in relation to the use of flow-describing equations. The ternary HNFs under research are composed of the nanomolecules aluminum oxide (Al2O3), copper oxide (CuO), silver (Ag), and water (H2O). For a number of significant physical characteristics, the physical situation is represented utilizing the boundary layer investigation, which produces partial differential equations (PDEs). The rheology of the movement is extended and computed in a revolving setting under the assumption that the movement is caused by a rotatingfloppy. Before the solution was found using the finite difference method, complicated generated PDEs were transformed into corresponding ODEs (Keller Box method). A rise in the implicated influencing factors has numerous notable physical impacts that have been seen and recorded. The Keller Box method (KBM) approach is also delivered for simulating the determination of nonlinear system problems faced in developing liquid and supplementary algebraic dynamics domains. The rate of entropy formation rises as the magnetic field parameter and radiation parameter increase. Entropy production rate decreases as the Brinkman number and Hall current parameter become more enriched. The thermal efficiency of ternary HNFs compared to conventional HNFs losses to a low of 4.8% and peaks to 5.2%.

Abstract It is well known that solar energy is the main source of thermal energy coming from the sun responsible for huge operations in engineering studies. It can be seen in the technology of photovoltaic cells, solar streetlights, solar energy plates, and solar water pumping. This study is for investigating solar radiation as well as a method to improve the performance of the solar water pump (SWP) with the use of solar radiation along with nanotechnology. The thermal transfer performance of the pump is checked for the case of many impacts including heat radiations and variable thermal conductivity. An Oldroyd‐B nanofluid with entropy production analysis has been scrutinized as a working coolant liquid in the system. Graphene oxide (GO) and Cu nanoparticles have been employed in engine oil (EO) as the base liquid. It is noticed that the heat transfer performance of SWP increases in the case of amplification in thermal radiation and temperature‐dependent thermal conductivity characteristics. In comparison to low thermal conductivity nanofluid, high thermal conductivity nanofluid provides the best capability for heat transmission. The thermal efficiency of the used (GO/EG) nanofluid has been enhanced by between 7.70% and 26.68% than (Cu/EO) nanofluid.

Abstract The second iteration of the optimal homotopy asymptotic technique (OHAM-2) has been protracted to fractional order partial differential equations in this work for the first time (FPDEs). Without any transformation, the suggested approach can be used to solve fractional-order nonlinear Zakharov–Kuznetsov equations. The Caputo notion of the fractional-order derivative, whose values fall within the closed interval [0, 1], has been taken into consideration. The method's appeal is that it provides an approximate solution after just one iteration. The suggested method's numerical findings have been contrasted with those of the variational iteration method, residual power series method, and perturbation iteration method. Through tables and graphs, the proposed method's effectiveness and dependability are demonstrated.

Abstract The purpose of this research was to estimate the thermal characteristics of tri-HNFs by investigating the impacts of ternary nanoparticles on heat transfer (HT) and fluid flow. The employment of flow-describing equations in the presence of thermal radiation, heat dissipation, and Hall current has been examined. Aluminum oxide (Al2O3), copper oxide (CuO), silver (Ag), and water (H2O) nanomolecules make up the ternary HNFs under study. The physical situation was modelled using boundary layer analysis, which generates partial differential equations for a variety of essential physical factors (PDEs). Assuming that a spinning disk is what causes the flow; the rheology of the flow is enlarged and calculated in a rotating frame. Before determining the solution, the produced PDEs were transformed into matching ODEs using the second order convergent technique (SOCT) also known as Keller Box method. Due to an increase in the implicated influencing elements, several significant physical effects have been observed and documented. For resembling the resolution of nonlinear system issues come across in rolling fluid and other computational physics fields.

Abstract In order to understand the characteristics of bio-convection and moving microorganisms in flows of magnetized Walters-B nano-liquid, we developed a model employing Riga plate with stretchy sheet. The Buongiorno phenomenon is likewise employed to describe nano-liquid motion in the Walters-B fluid. Expending correspondence transformations, the partial differential equation (PDE) control system has been transformed into an ordinary differential equation (ODE) control system. The COMSOL program is used to generate mathematical answers for non-linear equations by employing the Galerkin finite element strategy (G-FEM). Utilizing logical and graphical metrics, temperature, velocity, and microbe analysis are all studied. Various estimates of well-known physical features are taken into account while calculating nanoparticle concentrations. It is demonstrated that this model's computations directly relate the temperature field to the current Biot number and parameter of the Walters-B fluid. The temperature field is increased to increase the approximations of the current Biot number and parameter of the Walters-B fluid.

This study examined the flow of nanoliquid over an extendible surface in a micro-rotational manner. Nanotechnology recently prioritized nanoparticle dispersion in liquids. Nanoparticles increase the thermal conductivity of conventional liquids, which helps generate and transmit energy. The movement of energy has been chosen as a primary area of study in this examination via permeable oblique surface. Dufour impacts and thermal radiation have both been used in this investigation. Moreover, the viscous dissipative and magnetism force influences are considered on the porous medium. This work makes use of the popular bvp4c computational technique. A proper similarity conversion is managed to convert the flow expressions into nonlinearly differential equations. In the appearance of charts and tables, the physical values are depicted along with various consequences of material limitations. Based on the findings, we were able to determine that the Dufour and Eckert effects are responsible for the increase in the temperature profile contrary to the permeability of the inclined surface also Because of the angle of the surface, the velocity curve is found to be lower. This fundamental finding will help engineers and scientists manage the fluid flow and enhance sophisticated systems that employ it.

Prandtl Eyring fluid and stretchable wedge have multiple usages in many industries. The present study aims to investigate the impact of modified Buongiorno trihybrid nanofluid on Prandtl Eyring fluid past a wedge with the addition of various influences like endothermic/exothermic reactions, thermal radiation, and thermal conductivity, Cattaneo-Christov double diffusion. Aluminium alloys (AA7072), Aluminium alloys (AA7075) and Silver (Ag) are used as nanocomponents. Prandtl Eyring fluid is employed as a conventional liquid in the preparation of nanofluids by blending nano components into the base fluid. Further, the flow model is imposed with Modified Buongiorno nanofluid. By using the similarity approach, the proposed mathematical flow model of partial differential equations (PDEs) is turned into highly nonlinear ordinary differential equations (ODEs). Throughout the whole range of material parameters, the solution for the ensuing nonlinear boundary value issue is given by employing the finite element method (FEM). The numerical results of Prandtl Eyring ternary HNF motion, thermal and solute profiles are performed through graphical amassment on the collected data and discussed in detail. The numerical significances of material sections, such as the frictional force, local Nusselt quantity, and local Sherwood number requirements, are supplied in tabular form. Further, it also presents the validation and performance characteristics of the proposed device with previously published work and found excellent accuracy. In comparison to hybrid nanoparticles, the consequences reveal that heat transmission is amplified in the case of tri-hybrid nanoparticles. The numerical consequences show that the heat transfer amount reduces in the situation of exothermic reactions parameter Ω1.

To improve heat transfer, this work provides a unique theoretical mathematical model of ternary hybrid nanofluid. In this analysis, the tri-hybrid nanoparticles TiO2, Al2O3, and AA7072 are submerged in ethylene glycol (EG), resulting in the mixture TiO2+Al2O3+AA7072/EG. The tri hybridity nanofluid is considered 3-D flowing via a rotate permeable cone embedded in Darcy-Forchheimer porousness material in the existence of fluctuating temperature generating (sink) and current radiate fluxing. The Keller box scheme (KBS) is exploited to resolve the liquid flowing and temperature equations numerically after converting them to ordinary differential equations employing similarity transformations. The results are graphed, and it is shown that the tri-hybrid nanofluid (THNF) has superior thermal conductance to the hybrid nanofluid (HNF) and that the fluid's velocity and temperature develop as a consequence of enlargement in thermal radiative fluxing and variable thermal conductivity effects. Raising values of De and Fr decline drag friction but drag friction coefficient values are improved as a result of positive variation in M, Re, ς, and λ. It is apparent that the rate of heat transference amplifies owing to magnification in QT, QE and Rd but the heat transfer rate diminishes due to magnification in Re and Fr. Incremental change in volume fraction of nanoparticles φ=0.005 to 0.03 delivers more heat in the case of tri-HNFs TiO2+Al2O3+AA7072 in contrast to ethylene glycol based TiO2+Al2O3 fluid. The optimal percentage error diminishes for the drag friction phenomenon from 1.4% up to 1.1% by adopting De from 1 to 1.5 and λ=0.5. The percentage error in terms of heat transfer rate is getting smaller from 3.6% to 3.0% because of a positive change in QT by keeping Rd=1.5.

The goal of this research is to investigate the effects of Ohmic heating, heat generation, and viscous dissipative flow on magneto (MHD) boundary-layer heat transmission flowing of Jeffrey nanofluid across a stretchable surface using the Koo-Kleinstreuer-Li (KKL) model. Engine oil serves as the primary fluid and is suspended with copper oxide nanomolecules. The governing equations that regulate the flowing and heat transmission fields are partial-differential equations (PDEs) that are then converted to a model of non-linear ordinary differential equations (ODEs) via similarity transformation. The resultant ODEs are numerically resolved using a Keller box technique via MATLAB software that is suggested. Diagrams and tables are used to express the effects of various normal liquids, nanomolecule sizes, magneto parameters, Prandtl, Deborah, and Eckert numbers on the velocity field and temperature field. The outcomes display that the copper oxide-engine oil nanofluid has a lower velocity, drag force, and Nusselt number than the plain liquid, although the introduction of nanoparticles raises the heat. The heat transference rate is reduced by Eckert number, size of nanomolecules, and magneto parameter rising. Whilst, Deborah number is shown to enhance both the drag-force factor and the heat transfer rate. Furthermore, the discoveries reported are advantageous to upgrading incandescent lighting bulbs, heating, and cooling equipment, filament-generating light, energy generation, multiple heating devices, and other similar devices.

The dominant characteristics of hybrid nanofluids, such as low cost, improved heat transfer rates, and higher thermal and electrical conductivity, make them preferable fluids in thermal energy systems. In light of these incredible features, our goal in the present research is to analyse heat transfer and entropy generating in (Fe3O4–Cu)/water hybridity nano liquid flowing via a vertical cone with variable wall temperature inserted in a porous material. The effects of variable viscosity, magnetic force, and thermal radiative flux are additional aspects that contribute to the originality of the constructed model. The mathematical model is solved utilising the Crank-Nicolson technique, and the numerical findings are showed graphically and in a tabular manner. The heat transfer process is improved by hybrid nanoparticles and porosity while being hindered by magnetic interaction, viscosity, and thermal radiation. Energy loss in the form of increased entropy can be noted at the further vertical end of the cone than the base. The parametrical influence was reported to be nominal compared to the other physical aspects. Domination of heat transfer induced entropy generation and be observed for the porosity improvements.

Apart from the Buongiorno concept, no study was published that sufficiently examined the impact of nanoparticles on the extendable surface of the third-grade fluid prototype. The third grade nanofluid (3GNF) model's liquid simulation needs for Tiwari and Das are theoretically evaluated in the current work utilizing motor oil as the standard base liquid. Tiwari and Das' model look at the volume portion of nanoparticles for heat transfer enhancement as opposed to the Buongiorno concept, which primarily relies on thermophoretic and Brownian dispersion impacts. This analysis takes into consideration the Biot quantity, thermal radiative viscous flowing, slippage variable, Joule heating, and magneto variable, which are all thermal features of 3GNF. The Galerkin finite element methodology (G-FEM) mathematical structure is used to produce the computer solution. Copper/engine oil (Cu-EO) and titanium dioxide/engine oil (TiO2-EO) are considered. TiO2-EO nanofluid has a greater thermodynamic representation than Cu-EO nanofluid in the same conditions. The following rate range: 1.9%–43%, demonstrates Cu-advantage EO over TiO2-EO in terms of thermal conductivity. Additionally, the porous materials boundary's function is to increase the speed outlines whilst lowering the heating transduction rate. At the end of the day, the Reynolds and Brinkman values increase entropy.

The motive behind this article is to investigate the impact of triple diffusive convective flowing on Reiner-Philippoff (R-Ph) past a stretchable surface with Avramenko-Blinov-Shevchuk boundary restrictions. The governing determined partial differential equation (PDEs) are converted into ordinary differential equations (ODEs) with the utilization of similarity conversions and handled these equations computationally with the application of a well-recognized computational structure called Cash and Carp method. The dimensionless parameters used in figures and tables range between 0.1≤γ≤1.1, 0.1≤λ≤2.1, 0≤Nc1≤2, 0.1≤Nc2≤1.3, 0.1≤Le1,Le2,Ld1,andLd2≤2, 0.1≤Nd1≤0.5, 0.1≤Nd2≤0.5, 0≤Rd≤3, 0.1≤∊≤0.5, 0≤Nb≤1, 0≤Nt≤1.2. From numerical outcomes, it is revealed that the velocity field devalues outstanding to an incremental change in the Grashof number factor and the solutal profile escalates by the benefit of an intensification in the Dufour Lewis number. The heat of the fluid amplifies as a consequence of amplification in both linear heat radiation and Brownian diffusion parameters.

We present an innovative piecewise smooth mapping of the plane as a parametric discrete-time chaotic system that has robust chaos over a share of its significant organization parameters and includes the generalized Henon and Lozi schemes as two excesses and other arrangements as an evolution in between. To obtain the fractal Henon and Lozi system, the generalized Henon and Lozi system is defined by adopting the fractal idea (FHLS). The recommended system's dynamical performances are investigated from many angles, such as global stability in terms of the set of fixed points.

It is well known that there are two important classes of analytic functions of Ma-Minda type (MMT): Ma-Minda starlike and Ma-Minda convex functions. In this work, we suggest a new class of analytic functions, which is normalized in the open unit disk. The suggested class is generated by a roulette curve formula, which satisfies the symmetric behavior in the open unit disk. A roulette curve is shaped as the path outlined by the sum of two complex numbers, each affecting at a uniform rapidity in a circle. Special cases are illustrated involving special functions. Graphics of the curve are illustrated by using Mathematica 13.3.

Disease diagnosis with computer-aided methods has been extensively studied and applied in diagnosing and monitoring of several chronic diseases. Early detection and risk assessment of breast diseases based on clinical data is helpful for doctors to make early diagnosis and monitor the disease progression. The purpose of this study is to exploit the Convolutional Neural Network (CNN) in discriminating breast MRI scans into pathological and healthy. In this study, a fully automated and efficient deep features extraction algorithm that exploits the spatial information obtained from both T2W-TSE and STIR MRI sequences to discriminate between pathological and healthy breast MRI scans. The breast MRI scans are preprocessed prior to the feature extraction step to enhance and preserve the fine details of the breast MRI scans boundaries by using fractional integral entropy FIE algorithm, to reduce the effects of the intensity variations between MRI slices, and finally to separate the right and left breast regions by exploiting the symmetry information. The obtained features are classified using a long short-term memory (LSTM) neural network classifier. Subsequently, all extracted features significantly improves the performance of the LSTM network to precisely discriminate between pathological and healthy cases. The maximum achieved accuracy for classifying the collected dataset comprising 326 T2W-TSE images and 326 STIR images is 98.77%. The experimental results demonstrate that FIE enhancement method improve the performance of CNN in classifying breast MRI scans. The proposed model appears to be efficient and might represent a useful diagnostic tool in the evaluation of MRI breast scans.

Hybrid nanofluid (HNF) is a new and improved type of nanofluid models that is widely employed in fluid flow regimes to increase thermal efficiency. The purpose of this effort is to investigate HNF flow in two dimensions over a horizontal sheet while accounting for the effects of Joule heating, viscous dissipation, suction, and thermal slip. The impact of regulating parameters on skin friction and heat transfer is also investigated. HNF used in this investigation is a mixture of water and two types of solid nanoparticles, namely aluminium alloys AA7072 and AA7075. The numerical solutions of partial differential equations are obtained using the Crank-Nicolson method. The outcomes are illustrated in detailed ranges of the connection parameters. The thermal slip effect diminishes the temperature outline from the system and wall temperature. Shrinking sheet movement plays a key role in manipulating fluidity and thermal dispersal. Magnetic strength pulls down the fluidity and wall temperature meanwhile, it assists the thermal dispersion, fractional force, and Nusselt number.

Abstract A novel hybrid nanofluid was explored in order to find an efficient heat-transmitting fluid to replace standard fluids and revolutionary nanofluids. By using tangent hyperbolic hybrid combination nanoliquid with non-Newtonian ethylene glycol (EG) as a basis fluid and a copper (Cu) and titanium dioxide (TiO2) mixture, this work aims to investigate the viscoelastic elements of the thermal transferring process. Flow and thermal facts, such as a slippery extended surface with magnetohydrodynamic (MHD), suction/injection, form factor, Joule heating, and thermal radiation effects, including changing thermal conductivity, were also integrated. The Keller–Box method was used to perform collective numerical computations of parametric analysis using governing equivalences. In the form of graphs and tables, the results of TiO2–Cu/EG hybrid nanofluid were compared to those of standard Cu/EG nanofluid in important critical physical circumstances. The entropy generation study was used to examine energy balance and usefulness for important physically impacting parameters. Detailed scrutiny on entropy development get assisted with Weissenberg number, magnetic parameter, fractional volumes, injection parameter, thermal radiation, variable thermal conductivity, Biot number, shape variation parameter, Reynolds and Brinkman number. Whereas the entropy gets resisted for slip and suction parameter. In this case, spotted entropy buildup with important parametric ranges could aid future optimization.

In this paper, a type of complex algebraic differential equations (CADEs) is considered formulating by \[\alpha [\varphi(z) \varphi” (z) +(\varphi' (z))^2]+ a_m \varphi^m(z)+a_{m-1} \varphi^{m-1}(z)+...+ a_1 \varphi(z)+ a_0=0.\] The conformal analysis (angle-preserving) of the CADEs is investigated. We present sufficient conditions to obtain analytic solutions of the CADEs. We show that these solutions are subordinated to analytic convex functions in terms of $e^z.$ Moreover, we investigate the connection estimates (coefficient bounds) of CADEs by employing the majorization method. We achieve that the coefficients bound are optimized by Bernoulli numbers.

Abstract The central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli’s formula. As a consequence, some solutions are indicated by the well-known hypergeometric function. The class of starlike functions is investigated containing the suggested class.

Because of its multivariate particle suspension approach, the developing class of fluid has a better level of stability as well as increased heat transfer. In this regard, hybrid nanofluid outperforms ordinary fluid and even well-known nanofluid. In a slick environment, we investigate its fluidity and heat transfer qualities. Nano-leveled particle morphologies, porousness materials, variable thermal conductivity, slippage velocity, and thermal radiative effects are all being studied. The Galerkin finite element method is a numerical methodology for numerically solving the governing equations (G-FEM). For this analysis, a Powell-Eyring hybrid nanofluid (PEHNF) flowing via a permeable stretchable surface is used, which comprises two types of nanoparticles (NP), copper (Cu), and titanium alloy (Ti6Al4V) dispersed in sodium alginate (C6H9NaO7). The heat transfer ratio of PEHNF (Ti6Al4V-Cu/C6H9NaO7) remained much greater than that of conventional nanofluids (Cu-C6H9NaO7), with a range of 43%–54%. When lamina particles are present, the thermal conductivity of the boundary layer increases dramatically, while spherical nanoparticles have the lowest thermal conductivity. As nanoparticles are added under their fractional sizes, radiative heat conductance, and flexible heat conductance, the system’s entropy increases. The flow system’s ability to transport mass decreases when molecule diffusivity decreases dramatically. This is theoretically related to a rise in Schmidt number against molecular diffusivity.

The medical image enhancement is major class in the image processing which aims for improving the medical diagnosis results. The improving of the quality of the captured medical images is considered as a challenging task in medical image. In this study, a trace operator in fractional calculus linked with the derivative of fractional Rényi entropy is proposed to enhance the low contrast COVID-19 images. The pixel probability values of the input image are obtained first in the proposed image enhancement model. Then the covariance matrix between the input image and the probability of a pixel intensity of the input image to be calculated. Finally, the image enhancement is performed by using the convolution of covariance matrix result with the input image. The proposed enhanced image algorithm is tested against three medical image datasets with different qualities. The experimental results show that the proposed medical image enhancement algorithm achieves the good image quality assessments using both the BRISQUE, and PIQE quality measures. Moreover, the experimental results indicated that the final enhancement of medical images using the proposed algorithm has outperformed other methods. Overall, the proposed algorithm has significantly improved the image which can be useful for medical diagnosis process.

Convolution operators have profited in various areas of science. They are utilized in the investigations of computing techniques. A new convolution operator linked to a specific class of multi-valent meromorphic functions in the punctured unit disk (symmetric domain) is formulated. This analysis uncovers certain properties on the connections as well as the power series. We study a novel class of holomorphic functions concerning the recommended new operator. The second part of the outcome concerns the boundedness of the suggested difference structure given by the proposed operator. We focus on the Bloch space of meromorphic functions in the open unit disk. In this case, we use the spherical derivative. To obtain the maximum value of the polar derivative of the polynomials created by their partial sums, we use their partial sums as applications of the suggested operator.

A complex Layla and Majnun model system (CLMMS) is suggested in this study for a complex variable in the open-unit disk. Analytic solutions are discovered by using a technique of bounded turning functions. The set of necessary conditions is illustrated involving some special cases.

Introduction: The Internet of Things (IoT) comprises of various smart devices for the sharing of sensed data through online services. People will be directly contacted to check their health parameters and the reports will be collected centrally through smart devices. The requirement is protection of messages during the exchange of data between sender and receiver in order to tackle human malicious attacks. Various signature-based schemes are discussed in the literature to provide secure communication. Smart devices however require lightweight tasks by ensuring critical safety strengths. An important problem in the signature based method is that it incurs more computational expenses for signing and verification process in large numbers. Objectives: In this study, we introduced an efficient Short Signature Scheme (SSS) that uses Fractional Chaotic Map (FCM) for secure communication in IoT based smart devices, the security of which is closely related to a random oracle based on FCM assumption. Methods: In this study, we have designed new short signature scheme using FCM. The presented scheme consist of four sub-algorithm as follows: setup, key generation, signing and verification. We have used less rigorous operations based on the FCM to carry out signing and verification procedures, similar to human signing on valid documents and then verifying them as per witness. Results: The proposed SSS offers a better security assurance than currently established signature schemes. The key advantage of the SSS over the DSA schemes is that at the verification stage and signing period it takes less computation; it retains the degree of protection. The presented SSS takes less bandwidth for storage, communication, and computing resources; particularly applicable to wireless devices and smart cards. Conclusion: We concluded that the uses of fractional chaotic maps is more effective for secure communication in human-centered IoT to present a provably secure short signature technique.