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The motivation of this work is to analyse the nonlinear models and their complex nature with generalized tools associated with material and history-based properties. With the help of well-known and widely used numerical scheme, we study the stimulating behaviours of the financial system in this work. The impact of parameters on price index, rate of interest, investment demand, influence changes and investment cost with respect to saving amount, and the elasticity of commercial markets demand are discussed. The consequences of generalizing the model within the arbitrary order are derived. The existence of the solution for the considered system is presented. This study helps beginner researchers to investigate complex real-world problems and predict the corresponding consequences. [ABSTRACT FROM AUTHOR]

Malaria is spread by female Anopheles mosquitoes, which complete their life cycle by feeding on human blood. Parasites from the mosquito's saliva enter the human bloodstream through a mosquito bite. Thus, the link between humans and mosquitoes to parasites is established. According to WHO statistics, malaria appears widespread in tropical and subtropical locations around the equator, including most of Sub-Saharan Africa, Latin America. and Asia. The most prevalent causes of malaria transmission might be amicable temperature, which aids in the growth of the mosquito life-cycle, and a failure to maintain the local socio-economic condition, which reduces individual immunity. This study proposes the vector-host model to understand the spread of malaria infection. A vector model is used to understand the effects of temperature on the development of egg, larval, pupal, and adult mosquito populations. Furthermore, the role of immunity is being explored using the host model. Numerical simulations support the influence of temperature on disease transmission. The study draws attention to the fact that, along with issues like global warming and climate change. managing the socio-economic conditions of the area (healthcare facilities, environmental improvement) is essential for malaria eradication. [ABSTRACT FROM AUTHOR]

The pivotal aim of the present study is to find the solution for a nonlinear system describing the aggregation process of cellular slime mold by using q -homotopy analysis transform method. The coupled system is considered within the frame of the Caputo fractional operator. We examine three different cases with distinct values of sensitivity function χ ρ = 1 , ρ and ρ 2 to exemplify the efficiency and applicability of the considered scheme. We capture the nature of the obtained results with respect to the fractional order, with distinct initial conditions, and illustrate them using 2D and 3D plots for particular values of the parameters. The considered scheme offers parameters, which help to adjust the convergence region, and we plotted the ℏ-curves to dissipate the effect in the present framework. Moreover, some simulating and important behavior of the considered model using attained results shows the prominence of the hired operator while analyzing the coupled equations and confirms the competence of the projected scheme. [ABSTRACT FROM AUTHOR]

The solution for phytoplankton–toxic phytoplankton–zooplankton system with q-homotopy analysis transform method (q-HATM) is discussed. The projected system exemplifies three components (namely, zooplankton, toxic–phytoplankton as well as phytoplankton) and the corresponding nonlinear ordinary differential equations exemplify the zooplankton feeds on phytoplankton. The projected method is an amalgamation of q-homotopy analysis algorithm and Laplace transform and the derivative associated with the Atangana–Baleanu (AB) operator. The equilibrium points and stability have been discussed with the assistance of the Routh–Hurwitz rule in this work within the frame of generalized calculus. The fixed-point theorem is employed to present the existence and uniqueness of the attained result for the considered model, and we consider five different initial conditions for the projected system. Further, the physical nature of the achieved solution has been captured for fractional order, external force and diverse mass. The achieved consequences explicate that the proposed solution method is highly methodical, easy to implement and accurate to analyze the behavior of the nonlinear system relating to allied areas of science and technology. [ABSTRACT FROM AUTHOR]

The main goal of this study is to find solutions for the generalized coupled Ramani equation with the fractional order using the fractional natural decomposition method (FNDM). Four distinct cases are chosen to illustrate and validate the effectiveness of the considered method. The simulations in terms of numeric have been illustrated to confirm the reliability and proficiency of the projected scheme. Moreover, the behavior of the obtained results is captured for distinct fractional order. The comparison study is illustrated to verify the accuracy of the projected procedure. The achieved results exemplify that the projected solution procedure offers a simple algorithm and is also very efficient to analyze the nature of the coupled differential equations with arbitrary order situated in associated areas of Science and Engineering. [ABSTRACT FROM AUTHOR]

The main purpose of the present investigation is to find the solution of fractional coupled equations describing the romantic relationships using q -homotopy analysis transform method (q -HATM). The considered scheme is a unification of q -homotopy analysis technique with Laplace transform (LT). More preciously, we scrutinized the behavior of the obtained solution for the considered model with fractional-order, in order to elucidate the effectiveness of the proposed algorithm. Further, for the different fractional-order and parameters offered by the considered method, the physical natures have been apprehended. The obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems. [ABSTRACT FROM AUTHOR]

In present work, we investigate the numerical solution of time-fractional Jaulent–Miodek (JM) equations with the aid of two novel techniques namely, coupled fractional reduced differential transform method (CFRDTM) and q-homotopy analysis transform method (q-HATM). The obtained solutions are presented in a series form, which are converges rapidly. In order to verify the proposed techniques are reliable and accurate, the numerical simulations have been conducted in terms of absolute error. The obtained solutions are presented graphically to ensure the applicability and validity of the considered algorithms. The results of the study reveal that, the q-HATM is computationally very effective and accurate as compared to CFRDTM to analyse fractional nonlinear coupled JM equations. [ABSTRACT FROM AUTHOR]

The Atangana–Baleanu derivative and the Laguerre polynomial are used in this analysis to define a new computational technique for solving fractional differential equations. To serve this purpose, we have derived the operational matrices of fractional integration and fractional integro-differentiation via Laguerre polynomials. Using the derived operational matrices and collocation points, we reduce the fractional differential equations to a system of linear or nonlinear algebraic equations. For the error of the operational matrix of the fractional integration, an error bound is derived. To illustrate the accuracy and the reliability of the projected algorithm, numerical simulation is presented, and the nature of attained results is captured in diverse order. Finally, the achieved consequences enlighten that the solutions obtained by the proposed scheme give better convergence to the actual solution than the results available in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is graceful amalgamations of Laplace transform technique with q -homotopy analysis scheme and fractional derivative defined with Atangana–Baleanu (AB) operator. The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to illustrate and validate the efficiency of the future technique, we consider three different cases and analyzed the projected model in terms of fractional order. Moreover, the physical behavior of the obtained solution has been captured in terms of plots for diverse fractional order, and the numerical simulation is demonstrated to ensure the exactness. The obtained results elucidate that the proposed scheme is easy to implement, highly methodical as well as accurate to analyze the behavior of coupled nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to find the solution for special cases of regular-long wave equations with fractional order using q-homotopy analysis transform method (q-HATM). Design/methodology/approach: The proposed technique (q-HATM) is the graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme and fractional derivative defined with Atangana-Baleanu (AB) operator. Findings: The fixed point hypothesis considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional-order model. To illustrate and validate the efficiency of the future technique, the authors analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. Originality/value: To illustrate and validate the efficiency of the future technique, we analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. The obtained results elucidate that, the proposed algorithm is easy to implement, highly methodical, as well as accurate and very effective to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering. [ABSTRACT FROM AUTHOR]

A new solution for fractional extended Fisher–Kolmogorov (FEFK) equation using the q-homotopy analysis transform method (q-HATM) is obtained. The fractional derivative considered in the present work is developed with Atangana–Baleanu (AB) operator, and the technique we consider is a mixture of the q-homotopy analysis scheme and the Laplace transform. The fixed point hypothesis is considered for the existence and uniqueness of the obtained solution of this model. For the validation and effectiveness of the projected scheme, we analyse the FEFK equation in terms of arbitrary order for the two distinct cases. Moreover, numerical simulation is demonstrated, and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured. [ABSTRACT FROM AUTHOR]

In this paper, we examine the time-dependent two-dimensional cable equation of fractional order in terms of the Caputo fractional derivative. This cable equation plays a vital role in diverse areas of electrophysiology and modeling neuronal dynamics. This paper conveys a precise semi-analytical method called the q-homotopy analysis transform method to solve the fractional cable equation. The proposed method is based on the conjunction of the q-homotopy analysis method and Laplace transform. We explained the uniqueness of the solution produced by the suggested method with the help of Banach’s fixed-point theory. The results obtained through the considered method are in the form of a series solution, and they converge rapidly. The obtained outcomes were in good agreement with the exact solution and are discussed through the 3D plots and graphs that express the physical representation of the considered equation. It shows that the proposed technique used here is reliable, well-organized and effective in analyzing the considered non-homogeneous fractional differential equations arising in various branches of science and engineering. [ABSTRACT FROM AUTHOR]

This article presents the novel fractional-order Genesio–Tesi system, along with discussions of its boundedness, stability of the equilibrium points, Lyapunov stability, uniqueness of the solution and bifurcation. The efficient predictor–corrector approach is employed to quantitatively analyse the Genesio–Tesi system in fractional order. The findings enable conceptualisation and visualisation of the presented novel fractional-order Genesio–Tesi systems. The modified systems are proposed for future study on chaos control and applying the same for secure communication. Bifurcation analysis is carried out to see the variation in the system's behaviour from stability to chaos. The results of the bifurcation analysis support the results obtained for the stability of the equilibrium points. The system behaves chaotically since all the equilibrium points are unstable. The findings demonstrate a torus attractor for some of the suggested systems and a chaotic attractor for some of the novel fractional-order Genesio–Tesi systems. The system's torus attractor changes into a steady state when the order is reduced from integer to fractional. Changing the parameter values for one of the modified systems also shifts the system's behaviour, with the point attractor replacing the torus attractor. The point attractor of one of the systems changes into a steady character when the system's order is reduced from integer to fractional. The behaviour for one modified system is the same for fractional and integer orders. This discovery paves the way for the future study of the modified Genesio–Tesi system. This article gives a new direction to utilise these proposed Genesio–Tesi systems and study them extensively. The chaotic behaviour of the modified system can be used for secure communication. The synchronisation and chaos control of the modified system is recommended. [ABSTRACT FROM AUTHOR]

The pivotal aim of the present work is to obtain an approximated analytical solution for the fractional smoking epidemic model with the aid of a novel technique called q-homotopy analysis transform method (q-HATM). The considered nonlinear mathematical model has been effectively employed to elucidate the evolution of smoking in a population and its impact on public health in a community. We find some new approximate solutions in a series form, which converges rapidly, and the proposed algorithm provides auxiliary parameters, which are very reliable and feasible in controlling the convergence of obtained approximate solutions. Further, we present novel simulations for all cases of results to validate the applicability and effectiveness of proposed scheme. The outcomes of the study reveal that the q-HATM is computationally very effective to analyse nonlinear fractional differential equations arises in daily life problems. [ABSTRACT FROM AUTHOR]

In the present work, an efficient numerical technique, called q-homotopy analysis transform method (briefly, q -HATM), is applied to nonlinear Fisher's equation of fractional order. The homotopy polynomials are employed, in order to handle the nonlinear terms. Numerical examples are illustrated to examine the efficiency of the proposed technique. The suggested algorithm provides the auxiliary parameters ħ and n , which help us to control and adjust the convergence region of the series solution. The outcomes of the study reveal that the q -HATM is computationally very effective and accurate to analyse nonlinear fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we apply the q -homotopy analysis transform method to the mathematical model of the cancer chemotherapy effect in the sense of Caputo fractional. We find some new approximate numerical results for different values of parameters of alpha. Then, we present novel simulations for all cases of results conducted by considering the values of parameters of alpha in terms of two- and three-dimensional figures along with tables including critical numerical values. [ABSTRACT FROM AUTHOR]

In this paper, we have projected the theoretical and numerical investigation of the mathematical model representing the yellow fever virus transmission from infected mosquitoes to humans or vise-versa through mosquito bites in the framework of the Caputo derivative. Theoretical aspects of the dynamics of susceptible individuals, exposed individuals, infected individuals, toxic infected individuals, recovered and immune individuals, and susceptible mosquitoes and infected mosquitoes have been analyzed by using the theory of fractional calculus such as boundedness, uniqueness and existence of the solutions. Sufficient conditions for the global stability of the virus-free point of equilibrium are inspected. T validate the theoretical results numerical analysis is performed using the generalized Adams-Bashforth-Moultan method. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study and explore some characteristics of static perfect fluid space-time on paracontact metric manifolds. First, we show that if a K -paracontact manifold M 2 n + 1 is the spatial factor of a static perfect fluid space-time, then M 2 n + 1 is of constant scalar curvature − 2 n (2 n + 1) and squared norm of the Ricci operator is given by 4 n 2 (2 n + 1). Next, we prove that if a (κ , μ) -paracontact metric manifold M 2 n + 1 with κ > − 1 is a spatial factor of static perfect space-time, then for n = 1 , M 2 n + 1 is flat, and for n > 1 , M 2 n + 1 is locally isometric to the product of a flat (n + 1) -dimensional manifold and an n -dimensional manifold of constant negative curvature − 4. Further, we prove that if a paracontact metric 3-manifold M 3 with Q ϕ = ϕ Q is a spatial factor of static perfect space-time, then M 3 is an Einstein manifold. Finally, a suitable example has been constructed to show the existence of static perfect fluid space-time on paracontact metric manifold. [ABSTRACT FROM AUTHOR]

In this study, we investigate the infection system of the novel coronavirus (2019-nCoV) with a nonlocal operator defined in the Caputo sense. With the help of the fractional natural decomposition method (FNDM), which is based on the Adomian decomposition and natural transform methods, numerical results were obtained to better understand the dynamical structures of the physical behavior of 2019-nCoV. Such behaviors observe the general properties of the mathematical model of 2019-nCoV. This mathematical model is composed of data reported from the city of Wuhan, China. [ABSTRACT FROM AUTHOR]

In this article, the q -homotopy analysis transform method(q -HATM) is hired to find the solution for the time-fractional Klein–Fock–Gordon (FKFG) equation. The FKFG equation plays an important role in describing the relativistic electrons. To ensure the applicability and efficiency of proposed algorithm, we consider three cases of nonlinear FKFG equation. The uniqueness and convergence analysis for the projected problem is presented with the aid of Banach's fixed point theory. The numerical simulation has been presented to confirm the reliability and proficiency of the proposed scheme. Moreover, the behaviour of the obtained solution has been captured for diverse fractional order. The obtained results elucidate that, the proposed technique is easy to implement and very effective to analyse the behaviour complex problems arise in science and technology. [ABSTRACT FROM AUTHOR]

In the present investigation, the q-homotopy analysis transform method (q-HATM) is applied to find approximated analytical solution for the system of fractional differential equations describing the unsteady flow of a polytropic gas. Numerical simulation has been conducted to prove that the proposed technique is reliable and accurate, and the outcomes are revealed using plots and tables. The comparison between the obtained solutions and the exact solutions shows that the proposed method is efficient and effective in solving nonlinear complex problems. Moreover, the proposed algorithm controls and manipulates the obtained series solution in a huge acceptable region in an extreme manner and it provides us a simple procedure to control and adjust the convergence region of the series solution. [ABSTRACT FROM AUTHOR]

The study of nonlinear phenomena associated with physical phenomena is a hot topic in the present era. The fundamental aim of this paper is to find the iterative solution for generalized quintic complex Ginzburg–Landau (GCGL) equation using fractional natural decomposition method (FNDM) within the frame of fractional calculus. We consider the projected equations by incorporating the Caputo fractional operator and investigate two examples for different initial values to present the efficiency and applicability of the FNDM. We presented the nature of the obtained results defined in three distinct cases and illustrated with the help of surfaces and contour plots for the particular value with respect to fractional order. Moreover, to present the accuracy and capture the nature of the obtained results, we present plots with different fractional order, and these plots show the essence of incorporating the fractional concept into the system exemplifying nonlinear complex phenomena. The present investigation confirms the efficiency and applicability of the considered method and fractional operators while analyzing phenomena in science and technology. [ABSTRACT FROM AUTHOR]

In this paper, a solution of coupled fractional Navier–Stokes equation is computed numerically using the proposed q-homotopy analysis transform method (q-HATM), and the solution is found in fast convergent series. The given test examples illustrate the leverage and effectiveness of the proposed technique. The obtained results are demonstrated graphically. The present method handles the series solution in a large admissible domain in an extreme manner. It offers us a modest way to adjust the convergence region of the solution. Results with graphs explicitly reveal the efficiency and capability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely the q-homotopy analysis transform method. These equations play a vital role in describing the properties of shallow water waves through distinct dispersion relation. The convergence analysis and error analysis are presented in the present investigation for the future scheme. We illustrate two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to verify the accuracy. The numerical simulation is conducted to ensure the exactness of the future technique. The obtained numerical and graphical results are presented, the proposed scheme is computationally very accurate and straightforward to study and find the solution for fractional coupled nonlinear complex phenomena arising in science and technology. [ABSTRACT FROM AUTHOR]

In order to depict a situation of possible spread of infection from prey to predator, a fractional-order model is developed and its dynamics is surveyed in terms of boundedness, uniqueness, and existence of the solutions. We introduce several threshold parameters to analyze various points of equilibrium of the projected model, and in terms of these threshold parameters, we have derived some conditions for the stability of these equilibrium points. Global stability of axial, predator-extinct, and disease-free equilibrium points are investigated. Novelty of this model is that fractional derivative is incorporated in a system where susceptible predators get the infection from preys while predating as well as from infected predators and both infected preys and predators do not reproduce. The occurrences of transcritical bifurcation for the proposed model are investigated. By finding the basic reproduction number, we have investigated whether the disease will become prevalent in the environment. We have shown that the predation of more number of diseased preys allows us to eliminate the disease from the environment, otherwise the disease would have remained endemic within the prey population. We notice that the fractional-order derivative has a balancing impact and it assists in administering the co-existence among susceptible prey, infected prey, susceptible predator, and infected predator populations. Numerical computations are conducted to strengthen the theoretical findings. [ABSTRACT FROM AUTHOR]

In recent years, reaction–diffusion models have attracted researchers for their wide applications. In this article, we consider Brusselator reaction–diffusion system (BRDS), which is known for its cross diffusion and pattern formations in biology and chemistry. We derive an analytical solution of the fractional Brusselator reaction–diffusion system (FBRDS) with the help of the initial condition by a novel method, residual power series method (RPSM). The system solution has been analyzed by graph. [ABSTRACT FROM AUTHOR]

In this paper, we examined four different forms of generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili (B-KP)-like equations. In this connection, an accurate computational method based on the Riccati equation called sub-equation method and its Bäcklund transformation is employed. Using this method, numerous exact solutions that do not exist in the literature have been obtained in the form of trigonometric, hyperbolic, and rational. These solutions are of considerable importance in applied sciences, coastal, and ocean engineering, where the B–KP-like equations modeled for some significant physical phenomenon. The graph of the bright and dark solitons is presented in order to demonstrate the influence of different physical parameters on the solutions. All of the findings prove the stability, effectiveness, and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Medicinal leaves are playing a vital role in our everyday life. There are an enormous amount of species present in the world. Identification of each type would be a tedious task. Using image processing technology, we can overcome this problem by providing computer vision with the help of a convolution neural network (CNN). The objective of this research is to find out the best CNN model that helps in classifying the plant leaf species and identifying its category. In this research work, the proposed basic CNN model consisting of four convolution layers uses ten different medicinal leaf species each belonging to two categories providing an accuracy of 96.88%\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$96.88\%$$\end{document}. [ABSTRACT FROM AUTHOR]

In this paper we study the nature of Ricci solitons in a hyper generalized pseudosymmetric D-homothetically deformed Kenmotsu manifold. [ABSTRACT FROM AUTHOR]