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The current manuscript investigates a six compartmental mathematical model for malicious Codes in Wireless Sensor Network is consider for investigation under the fractional operator of Caputo along with their numerical scheme. The six agent nodes of the network sensors are transferable like in infection with in their community of different nodes. With the help of fixed point theory the presentation of existence and uniqueness of solution of the said model are also given. The scheme of numerical solution under fractional format is developed with the choice of fractional orders which increasing the degree of freedom for such type of network analysis. The numerical simulation of all the six agents are given on different fractional orders along with sensitivity of the fractional orders and some used parameters. The new analysis artificial neural network (ANN) method has been utilized for the considered model and compared with Adams–Bashforth (AB) method. We divided the data set into three categories training, testing and validation with ANN method and the analysis is presented in this work. [ABSTRACT FROM AUTHOR]

Invasive‐invaded species problems are of relevance in mathematics applied to population dynamics. In this paper, the mentioned dynamics is introduced based on a fourth‐order parabolic operator, together with coupled non‐linear reaction terms. The fourth‐order operator allows us to model a heterogeneous diffusion, as introduced by the Landau–Ginzburg free energy approach. The reaction terms are given by a coupled non‐linear effect in the invasive species, to account for the action of the invaded species and limited resources, and by a non‐Lipschitz term in the invaded species, to account for possible sprouts, once the invasion occurs. The analysis starts by the proof of existence and uniqueness of solutions, making use of the semi‐group theory and a fixed point argument. Asymptotic solutions to the invasive species are explored with an exponential scaling. Afterward, the problem is analyzed with traveling wave profiles, for which a region of positive solutions is explored. [ABSTRACT FROM AUTHOR]

In fixed point theory, interpolation is acknowledged in numerous areas of research, for instance, earth sciences, metallurgy, surface physics, and so on because of its prospective applications in the estimation of signal sensation analysis. As a result, it is interesting to investigate the fixed point and fixed circle (disc) utilizing interpolative techniques via partial b‐metric spaces in which non‐trivial as well as real generalizations are feasible. We define some improved interpolative contractions to create an environment for the existence of a fixed point and fixed circle and solve a two‐point boundary value problem related to a differential equation of second order. The obtained conclusions are validated by providing illustrative examples. Determining the fixed point of a non‐self mapping, the uniqueness of the fixed point and fixed circle, and the study of fractal interpolants would also be a fascinating investigation in the time to come. [ABSTRACT FROM AUTHOR]

Coronavirus has paralyzed various socio‐economic sectors worldwide. Such unprecedented outbreak was proved to be lethal for about 1,069,513 individuals based upon information released by Worldometers on October 09, 2020. In order to fathom transmission dynamics of the virus, different kinds of mathematical models have recently been proposed in literature. In the continuation, we have formulated a deterministic COVID‐19 model under fractional operators using six nonlinear ordinary differential equations. Using fixed‐point theory and Arzelá Ascoli principle, the proposed model is shown to have existence of unique solution while stability analysis for differential equations involved in the model is carried out via Ulam–Hyers and generalized Ulam–Hyers conditions in a Banach space. Real COVID‐19 cases considered from July 01 to August 14, 2020, in Pakistan were used to validate the model, thereby producing best fitted values for the parameters via nonlinear least‐squares approach while minimizing sum of squared residuals. Elasticity indices for each parameter are computed. Two numerical schemes under singular and non‐singular operators are formulated for the proposed model to obtain various simulations of particularly asymptomatically infectious individuals and of control reproduction number Rc. It has been shown that the fractional operators with order α=9.8254e−01 generated Rc=2.5087 which is smaller than the one obtained under the classical case (α=1). Interesting behavior of the virus is explained under fractional case for the epidemiologically relevant parameters. All results are illustrated from biological viewpoint. [ABSTRACT FROM AUTHOR]

It is comprehended that the systems without any limitation on their Zeno action are enthralled in a vast class of hybrid systems. This article is influenced by a new category of nonautonomous second‐order measure differential problems with state‐dependent delay (SDD) and noninstantaneous impulses (NIIs). Some new sufficient postulates are created that guarantee the solvability and approximate controllability. We employ the fixed point strategy and theory of Lebesgue–Stieltjes integral in the space of piecewise regulated functions. The measure of noncompactness is applied to establish the existence of a solution. Moreover, the measured differential equations generalize the ordinary impulsive differential equations. Thus, our findings are more prevalent than that encountered in the literature. At last, an example is comprised that exhibits the significance of the developed theory. [ABSTRACT FROM AUTHOR]

Nowadays, the complete world is suffering from untreated infectious epidemic disease COVID‐19 due to coronavirus, which is a very dangerous and deadly viral infection. So, the major desire of this task is to propose some new mathematical models for the coronavirus pandemic (COVID‐19) outbreak through fractional derivatives. The adoption of modified mathematical techniques and some basic explanation in this research field will have a strong effect on progressive society fitness by controlling some diseases. The main objective of this work is to investigate the dynamics and numerical approximations for the recommended arbitrary‐order coronavirus disease system. This system illustrating the probability of spread within a given general population. In this work, we considered a system of a novel COVID‐19 with the three various arbitrary‐order derivative operators: Caputo derivative having the power law, Caputo–Fabrizio derivative having exponential decay law and Atangana–Baleanu‐derivative with generalized Mittag–Leffler function. The existence and uniqueness of the arbitrary‐order system is investigated through fixed‐point theory. We investigate the numerical solutions of the non‐linear arbitrary‐order COVID‐19 system with three various numerical techniques. For study, the impact of arbitrary‐order on the behavior of dynamics the numerical simulation is presented for distinct values of the arbitrary power β. [ABSTRACT FROM AUTHOR]

We prove the existence of periodic traveling wave solutions for general discrete nonlinear Klein‐Gordon systems, considering both cases of hard and soft on‐site potentials. In the case of hard on‐site potentials, we implement a fixed‐point theory approach, combining Schauder's fixed‐point theorem and the contraction mapping principle. This approach enables us to identify a ring in the energy space for nontrivial solutions to exist, energy (norm) thresholds for their existence, and upper bounds on their velocity. In the case of soft on‐site potentials, the proof of existence of periodic traveling wave solutions is facilitated by a variational approach based on the mountain pass theorem. Thresholds on the averaged kinetic energy for these solutions to exist are also derived. [ABSTRACT FROM AUTHOR]

The primary focus of this article is to provide sufficient conditions for the controllability of Hilfer fractional neutral integrodifferential systems. By using the theories on fractional calculus, semigroup theory, and fixed point theorem method, the results are proved through integral contractors for the nonlinear neutral evolution equation in a non‐dense domain. In the end, the derived outcomes are validated through suitable illustrations. [ABSTRACT FROM AUTHOR]

In this article, we establish new fixed ellipse theorems that will provide a geometrical perspective to the classical metric fixed point theory. Also, we provide novel fixed ellipse consequences as the expanding of some existing and known fixed circle theorems in literature to ellipse case, and give non‐trivial illuminating examples, which show the impressiveness of our results. On the other hand, using the given fixed ellipse, we give some solutions for the open question which is posed by Rhoades with respect to the presence of contractive mappings that permissive discontinuity at the fixed point. Furthermore, we give an application to usage respecting activation functions handled at neural networks via the discontinuity and the obtained results of fixed ellipse. [ABSTRACT FROM AUTHOR]

In this paper, we study a system of multiple positive solutions and stability results for nonlinear fractional delay differential equations involving p$$ p $$‐Laplacian operator. We derived adequate conditions to ensure that at least three nonnegative solutions exist by applying the conditions of the Leggett–Williams fixed‐point theory and some Green function properties. Due to a small change in time‐delay, we analyzed the Hyers–Ulam stability‐type of the equation. We used Riemann–Liouville fractional differential definition, and we assumed that nonzero delay ϑ>0$$ \vartheta >0 $$. In addition, for application purpose, comprehensive examples are given to ensure the effectiveness and feasibility of the results in this paper. Our proposed equation generalize some literature in the system. [ABSTRACT FROM AUTHOR]

This article investigates the exact and approximate controllability, finite time stability, and B$$ \mathcal{B} $$–Hyers–Ulam–Rassias stability of a neutral impulsive system of differential equations with two delays. Fixed point theory is associated in the analysis of controllability of the system. The stability analysis is carried out with the help of Grönwall type inequality. [ABSTRACT FROM AUTHOR]

The solutions to fractional differential equations are a developing area of current research, given that these equations arise in various domains. In this article, we provide some necessary criteria for the existence, uniqueness, and different types of Ulam stability for a coupled implicit system requiring the conditions for nonlocal Riemann–Liouville and Erdélyi–Kober q‐fractional integral conditions. The uniqueness and existence results for the suggested coupled system are demonstrated using Banach fixed point theorem and Leray–Schauder of cone type. We also explore the various types of stability using classical methods of nonlinear functional analysis. To verify the effectiveness of our theoretical outcomes, we study an interesting example. [ABSTRACT FROM AUTHOR]

The author considers a class of nonlocal convolution‐type ordinary differential equations of the form −Aa∗(g∘u)(1)u′′(t)=λft,u(t),0

A kind of nonlinear noninstantaneous impulsive equation with state‐dependent delay is studied here. By utilizing suitable fixed point theorem and the theory of semigroup in Banach space, the uniqueness and existence results of S$$ \mathcal{S} $$‐asymptotically w$$ w $$‐periodic mild solutions are obtained, respectively. In the end, two examples are presented to demonstrate the validity of the obtained results. [ABSTRACT FROM AUTHOR]

Rotavirus infection is also a major cause of death in babies and children. Rotavirus causes severe diarrhea in babies and infants in developed and underdeveloped countries. It has multiple types of transmission: human to human and human to the environment. This paper investigates the time‐fractional order rotavirus epidemic model in an uncertain environment defined in the Caputo–Fabrizio (CF) derivative sense. In the titled model, the initial conditions are considered as fuzzy numbers. A double parametric form (DPF) of fuzzy numbers has been used in the fuzzy fractional rotavirus model. A semi‐analytical approach called the homotopy perturbation Elzaki transform method (HPETM) has been employed to solve the present model with the fuzzy initial condition. In order to derive the existence and uniqueness of the solution of the model, the concept of fixed‐point theory is utilized. Various fuzzy and interval solutions have been computed by considering different values of fractional orders, fuzzy parameters, and parameters involved in the given model. [ABSTRACT FROM AUTHOR]

The first symptomatic infected individuals of coronavirus (Covid‐19) was confirmed in December 2020 in the city of Wuhan, China. In India, the first reported case of Covid‐19 was confirmed on 30 January 2020. Today, coronavirus has been spread out all over the world. In this manuscript, we studied the coronavirus epidemic model with a true data of India by using Predictor‐Corrector scheme. For the proposed model of Covid‐19, the numerical and graphical simulations are performed in a framework of the new generalised Caputo sense non‐integer order derivative. We analysed the existence and uniqueness of solution of the given fractional model by the definition of Chebyshev norm, Banach space, Schauder's second fixed point theorem, Arzel's‐Ascoli theorem, uniform boundedness, equicontinuity and Weissinger's fixed point theorem. A new analysis of the given model with the true data is given to analyse the dynamics of the model in fractional sense. Graphical simulations show the structure of the given classes of the non‐linear model with respect to the time variable. We investigated that the mentioned method is copiously strong and smooth to implement on the systems of non‐linear fractional differential equation systems. The stability results for the projected algorithm is also performed with the applications of some important lemmas. The present study gives the applicability of this new generalised version of Caputo type non‐integer operator in mathematical epidemiology. We compared that the fractional order results are more credible to the integer order results. [ABSTRACT FROM AUTHOR]

Novel coronavirus (COVID‐19), a global threat whose source is not correctly yet known, was firstly recognised in the city of Wuhan, China, in December 2019. Now, this disease has been spread out to many countries in all over the world. In this paper, we solved a time delay fractional COVID‐19 SEIR epidemic model via Caputo fractional derivatives using a predictor–corrector method. We provided numerical simulations to show the nature of the diseases for different classes. We derived existence of unique global solutions to the given time delay fractional differential equations (DFDEs) under a mild Lipschitz condition using properties of a weighted norm, Mittag–Leffler functions and the Banach fixed point theorem. For the graphical simulations, we used real numerical data based on a case study of Wuhan, China, to show the nature of the projected model with respect to time variable. We performed various plots for different values of time delay and fractional order. We observed that the proposed scheme is highly emphatic and easy to implementation for the system of DFDEs. [ABSTRACT FROM AUTHOR]

In this study, we apply the fractional Laplace variational iteration method (FLVIM), a computer methodology for exploring fractional Navier–Stokes equation solutions. In light of the theory of fixed points and Banach spaces, this paper also explores the uniqueness and convergence of the solution of general fractional differential equations obtained by the suggested method. In addition, the fractional Laplace variational iteration method solution's error analysis is covered. The computational technique also clearly demonstrates the validity and dependability of the suggested method for solving fractional Navier‐Stokes equations. Furthermore, the obtained solutions are a perfect fit with previously established solutions. [ABSTRACT FROM AUTHOR]

In this paper, the ABC fractional derivative is used to provide a mathematical model for the dynamic systems of substance addiction. The basic reproduction number is investigated, as well as the equilibrium points' stability. Using fixed point theory and nonlinear analytic techniques, we verify the theoretical results of solution existence and uniqueness for the proposed model. A numerical technique for getting the approximate solution of the suggested model is established by using the Adams type predictor‐corrector rule for the ABC‐fractional integral operator. There are several numerical graphs that correspond to different fractional orders. Furthermore, we present a numerical simulation for the transmission of substance addiction in two scenarios with fundamental reproduction numbers greater than and fewer than one. [ABSTRACT FROM AUTHOR]

In this paper we investigate the Cauchy problem for a fractional diffusion equation and the time‐fractional derivative is taken in the Caputo type sense. We give a representation of solutions under Fourier series and analyze initial value problems for the semi‐linear fractional diffusion equation with a memory term. We also discuss the stability of the fractional derivative order for the time under some assumptions on the input data. Our key idea is to use Mittag‐Leffler functions, the Banach fixed point theorem, and some Sobolev embeddings. [ABSTRACT FROM AUTHOR]

The prime aim of the present paper is to continue developing the theory of tempered fractional integrals and derivatives of a function with respect to another function. This theory combines the tempered fractional calculus with the Ψ$$ \Psi $$‐fractional calculus, both of which have found applications in topics including continuous time random walks. After studying the basic theory of the Ψ$$ \Psi $$‐tempered operators, we prove mean value theorems and Taylor's theorems for both Riemann–Liouville‐type and Caputo‐type cases of these operators. Furthermore, we study some non‐linear fractional differential equations involving Ψ$$ \Psi $$‐tempered derivatives, proving existence‐uniqueness theorems by using the Banach contraction principle and proving stability results by using Grönwall type inequalities. [ABSTRACT FROM AUTHOR]

This paper deals with some existence and Ulam stability results for some classes of implicit fractional q$$ q $$‐difference equations with and without random effects in Banach spaces and Banach algebras. Our results are provided by applying the fixed point theory (Itoh's random fixed point theorem, the nonlinear alternative of Schaefer's type proved by Dhage, and an other Dhage's random fixed point theorem in Banach algebras). Other results about the extremal solutions and random extremal solutions under Carathéodory and certain monotonicity conditions are proved. In the final section, some illustrative examples are provided. [ABSTRACT FROM AUTHOR]

In this work, we synthesize orthogonal and bipolar metric issues and tried to deal with them in fuzzy metric spaces. We introduce a new concept of orthogonal fuzzy bipolar metric space and prove some fixed point theorems for some contractions in this space. Also, we provide some examples to illustrate the validity of the results obtained in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose a reaction–diffusion predator–prey model with fear effect under a predator‐poisoned environment. First, we analyze the existence and stability of constant positive steady states. Second, taking the cost of minimum fear as the bifurcation parameter, the direction and stability of spatially homogeneous/inhomogeneous periodic solutions are investigated. Then, some properties of nonconstant positive steady states are investigated, such as nonexistence, existence, and steady state bifurcation. Applying the fixed point index theory, the existence of the nonconstant positive steady state is discussed, indicating that the proper diffusion rate of prey and larger diffusion rate of predator are beneficial to survival of populations. Moreover, taking the diffusion rate of predator as the bifurcation parameter, the steady state bifurcations from simple and double eigenvalues are intensively established. At last, the validity of the theoretical analysis is verified by numerical simulations. Biological interpretation reveals that the fear effect and the diffusion rate of populations can lead to the emergence of Hopf and steady state bifurcation, thereby destroying the stability of populations and promoting the benign evolution of populations. [ABSTRACT FROM AUTHOR]

A new approximate solution of the fractional nonlinear integrable single sixth order Drinfeld–Sokolov–Satsuma–Hirota (DSSH) equation is introduced and depicted. The q‐homotopy analysis transform method (q‐HATM) is a powerful algorithm to solve such problem. The proposed algorithm offers an approximate solution that is very close to the exact solution while avoiding the complexity that exists in many other methods. With the help of Banach's fixed‐point theory, the uniqueness theorem and convergence analysis of the anticipated issue are discussed. The normal frequency for the fractional solution to this problem differs by the difference in the fractional derivative. [ABSTRACT FROM AUTHOR]

The investigation of existence and uniqueness of impulsive dynamical fractional systems with quadratic perturbation of second type subject to nonlocal boundary conditions is presented and proved. By employing the fractional theory, Banach contraction technique, and Krasnoselskii's fixed point theorem, we derived some sufficient conditions to ensure the existence of our system. An example is offered to enhance the applicability of the results obtained. [ABSTRACT FROM AUTHOR]

Non‐classical logicians do not typically reject classically valid logical principles across the board. In fact, they sometimes suggest that their preferred logic recovers classical reasoning in most circumstances. This idea has come to be known in the literature as 'classical recapture'. Recently, classical logicians have raised various doubts about it. The main problem is said to be that no rigorous explanation has been given of how is it exactly that classical logic can be recovered. The goal of the paper is to address this problem. First, I discuss a number of different ways to characterize the idea of classical recapture and I examine how far it can be pushed. Secondly, I argue that a palatable form of classical recapture is given by the thought that classical logic can be retained for statements that are grounded (in Kripke's sense). To substantiate this view I provide a formal fixed‐point semantics for a language containing a predicate standing for the concept of groundedness and I address a couple of objections that have been deployed against the claim that classical recapture can aid the non‐classical logician's cause. [ABSTRACT FROM AUTHOR]

Anti‐abortion violence ('AAV') is anathema to almost everyone, on all sides of the abortion debate. Yet, as this article aims to show, it is far more difficult than has previously been recognised to avoid the deeply unpalatable conclusion that it can sometimes be justified. Some of the most frequently‐occupied positions on the morality of abortion will imply precisely that conclusion, I argue, unless conjoined with an especially stringent and unattractive form of pacifism. This is true not only of strict anti‐abortion views, but also, more surprisingly, of some of the most familiar and influential moderate defences of abortion rights. The latter conclusion raises the question, which further work will be required to fully resolve, of what our account of abortion ethics and prenatal moral status must be if it is to enable reconciliation of the common‐sense rejections of both pacifism and AAV. I end with reasons to expect that the path to an account that satisfies this demand, without generating further significant intuitive problems, will be far from straightforward. [ABSTRACT FROM AUTHOR]

In this paper, we present Banach, Kannan, Chatterjea, and Reich‐type contractive inequalities for multivalued mappings and prove the existence of their common fixed points in a complete metric space without assuming compactness of the images under those mappings. [ABSTRACT FROM AUTHOR]

This paper proposes a novel guidance law based on model predictive control for protecting an aircraft from a homing missile. Considering that in the target‐missile‐defender engagement the attacking missile is pursuing the target aircraft by employing a known linear guidance law, a non‐linear predictive model for the engagement is established. This predictive model allows converting the three‐body engagement to a one‐on‐one engagement. The time‐to‐go for the defender towards the future position of the incoming missile is analytically derived, indicating that the optimal time for the defender to intercept the incoming missile is a fixed‐point of a real‐valued function. As a result, the optimal interception duration can be obtained by a standard fixed‐point iteration method, and thus the interception point can be readily predicted via integrating the predictive model. The guidance command is generated by directly leading the defender to the predicted intercept point. Numerical simulations in different scenarios validate the algorithm to be computationally efficient, and demonstrate that the proposed strategy outperforms previous techniques in terms of miss distance, engagement duration, and the control effort. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the uniform stability for a class of fuzzy fractional‐order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in 12,1. However, the case of the fractional‐order belonging to (0,12) has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective. [ABSTRACT FROM AUTHOR]

In this article, we introduce a class of fuzzy matrix valued control functions and we apply the Radu–Miheţ method derived from an alternative fixed point theorem to investigate the UHML stability for a class of ξ‐Hilfer fractional differential equations in matrix valued fuzzy Banach (MVFB) spaces. An example is given to illustrate the UHML stability for a fractional system. [ABSTRACT FROM AUTHOR]

In the current article, controllability and stability analysis of a system of differential equations is investigated. The system is governed by semilinear impulsive differential equations of second order with two delays. Controllability is studied using Rothe's fixed point theory while stability analysis is carried out with the help of Grönwall inequality and some other conditions. Fixed point approach is incorporated in determination of uniqueness of solution. [ABSTRACT FROM AUTHOR]

In this manuscript, our primary focus on the approximate controllability outcomes for non‐densely defined Sobolev‐type Hilfer fractional neutral differential system with infinite delay. By applying the findings and facts associated with fractional theory and the fixed‐point method, the principal discussions are demonstrated. First, we focus on the existence and then discuss the approximate controllability. At last, we provide an example for the demonstration of theory. [ABSTRACT FROM AUTHOR]

In this paper, we are mainly concerned with the unstirred chemostat model with variable yield. We first study positive steady‐state solution and its stability of the model by bifurcation theory and the fixed point index theory. Then we focus on the model with perturbation on diffusion rates, nonconstant yield rate, and nonzero death rate to obtain the existence and stability of the unique positive solution, whenever the constants are perturbed from the critical point. [ABSTRACT FROM AUTHOR]

We study a nonlocal evolution equation generalising a model introduced by Shigeru Kondo to explain colour patterns on a skin of a guppy fish. We prove the existence of stationary solutions using either the bifurcation theory or the Schauder fixed‐point theorem. We also present numerical studies of this model and show that it exhibits patterns similar to those modelled by well‐known reaction‐diffusion equations. [ABSTRACT FROM AUTHOR]

This paper deals with the existence, nonexistence, and multiplicity of positive solutions of the coupled system of Riemann‐Liouville fractional differential equations together with multipoint boundary conditions containing fractional derivatives at nonlocal points. We use the theory of fixed point index approach to prove our results exhibiting the existence and the nonexistence of positive solutions. [ABSTRACT FROM AUTHOR]

Many evolutionary processes from various fields of physical and engineering sciences undergo abrupt changes of state at certain moments of time between intervals of continuous evolution. These processes are more suitably modeled by impulsive differential equations. In this paper, we study the controllability of an impulsive fractional differential equation with infinite state‐dependent delay in an arbitrary Banach space. We apply semigroup theory and Schaefer fixed point theorem. As an application, we include an example to illustrate the theory. [ABSTRACT FROM AUTHOR]

The dynamics of diseases and effectiveness of control policies play important role in the prevention of epidemic diseases. To this end, this paper is concerned with the design of fractional order coronavirus disease (COVID‐19) model with Caputo Fabrizio fractional derivative operator of order Ω ∈ (0, 1] for the COVID‐19. Verify the nonnegative special solution and convergence of the scheme with in the domain. Caputo‐Fabrizio technique apply with Sumudu transformation method is used to solve the fractional order COVID‐19 model. Fixed point theory and Picard Lindelof approach are used to provide the stability and uniqueness of the results. Numerical simulations conspicuously demonstrate that by applying the proposed fractional order model, governments could find useful and practical ways for control of the disease. [ABSTRACT FROM AUTHOR]

In this work we present and analyze a fully‐mixed formulation for the nonlinear model given by the coupling of the Navier–Stokes and Darcy–Forchheimer equations with the Beavers–Joseph–Saffman condition on the interface. Our approach yields non‐Hilbertian normed spaces and a twofold saddle point structure for the corresponding operator equation. Furthermore, since the convective term in the Navier–Stokes equation forces the velocity to live in a smaller space than usual, we augment the variational formulation with suitable Galerkin type terms. The resulting augmented scheme is then written equivalently as a fixed point equation, so that the well‐known Schauder and Banach theorems, combined with classical results on nonlinear monotone operators, are applied to prove the unique solvability of the continuous and discrete systems. In particular, given an integer k ≥ 0, Raviart–Thomas spaces of order k, continuous piecewise polynomials of degree ≤k + 1 and piecewise polynomials of degree ≤k are employed in the fluid for approximating the pseudostress tensor, velocity and vorticity, respectively, whereas Raviart–Thomas spaces of order k and piecewise polynomials of degree ≤k for the velocity and pressure, constitute a feasible choice in the porous medium. A priori error estimates and associated rates of convergence are derived, and several numerical examples illustrating the good performance of the method are reported. [ABSTRACT FROM AUTHOR]

This paper aims to study the sufficient conditions for the existence and uniqueness of solutions to the multipoint coupled boundary value problem of nonlinear Caputo–Hadamard fractional differential equations associating with nonlocal integral boundary conditions. The required conditions are obtained by using classical results of functional analysis and fixed point theory. Furthermore, the Hyers–Ulam stability of solutions is discussed, and sufficient conditions for the stability are developed. Obtained results are supported by examples and illustrated in the last section. [ABSTRACT FROM AUTHOR]

New coexistence fixed point theorems in product Banach spaces are established via the classical theory of fixed point index for compact maps defined on cones. Each component of a coexistence fixed point is nonzero. These coexistence fixed point theorems are applied to obtain results on coexistence solutions of systems of Hammerstein integral equations, second‐order ordinary differential equations with general separated boundary conditions, and one‐dimensional competition model of Ricker types. [ABSTRACT FROM AUTHOR]

In this century when computers and other electronic devices have taken over the world, the rate at which malwares including viruses are infecting these devices has also started to increase rapidly. The developments of computer systems and its ever increasing uses require preventing strategies of malwares. This study aims to analyze an epidemiological model on the spread of computer viruses. We investigated the existence and uniqueness of solutions, examined the stability of the model, and performed numerical simulations. First, a model has been extended with the help of Atangana–Baleanu fractional derivative in Caputo sense. Then, the fixed point approach has been adopted to investigate the existence and uniqueness of solution of the model. Furthermore, the stability of the model has been examined with the help of the Hyers–Ulam stability method, and the model's numerical solutions have been obtained with the help of the Adam–Bashforth method. Lastly, the model's simulations have been performed considering various fractional derivative values. [ABSTRACT FROM AUTHOR]

In this manuscript, we investigate the existence and the semi‐analytical solutions of the fractional‐order vector‐born disease model using the Caputo–Fabrizio fractional derivative. In this study, we have developed existence results about the solution for the problem under consideration using the results of fixed‐point theory. On the other hand, the semi‐analytical results were obtained via Laplace Adomain decomposition method. The results established using the proposed techniques are in the form of an infinite series which converges rapidly to the exact solution. Furthermore, the obtained results are compared with the result of integer‐order derivatives. The dynamics of the solution is interpreted graphically. [ABSTRACT FROM AUTHOR]

For q≥1 we consider the nonlocal ordinary differential equation −a∫01|y|qdsy′′(t)=λf(t,y(t)),0

This paper is concerned with a class of fractional partial functional differential equations with nonlocal conditions in Banach spaces. By using the theories of resolvent operator, the Schauder fixed point theorem and the Banach contraction mapping principle, we obtain the sufficient conditions for the local and global existence of the mild solution. [ABSTRACT FROM AUTHOR]

In this paper, we characterize a new generalization of Perov fixed point result via Λ‐admissibility and Ψ‐contractivity on vector‐valued metric space and provide a comparative example. Then we investigate the existence of solution of a complex partial differential equation of the form, ∂z¯w=Fz,w,∂zw,via obtained new fixed point results under suitable conditions. [ABSTRACT FROM AUTHOR]

The main objective of this research work is to establish existence results as well as to study qualitative aspects of the proposed coupled system of fractional hybrid delay differential equations (FHDDEs). Using the hybrid fixed point theory, we establish appropriate results for the existence of at least one solution to our problem. The powerful tools of functional analysis and dynamical systems are applied to derive different kinds of stability analysis. These include Ulam‐Hyers (UH), generalized Ulam‐Hyers (GUH), Ulam‐Hyers‐Rassias (UHR), and generalized Ulam‐Hyers‐Rassias (GUHR). In order to provide the authenticity of the our results, an illustrative example is given to wind up the present research work. [ABSTRACT FROM AUTHOR]

This paper first puts forward the concept of global polynomial stabilization (GPS) of coupled neural networks (CNNs) with multi‐proportional delays. First, the existence and uniqueness of the equilibrium point of the proposed CNNs are proved by using homeomorphic mapping theorem. Second, by taking discrete controller, based on Lyapunov functionals and linear matrix inequality (LMI) skills, we gain several delay‐dependent GPS and global asymptotic stabilization (GAS) criteria for the proposed system, and these criteria can be validated by Matlab. The relationship among GPS, global exponential stabilization (GES), and GAS is also revealed. In the end, our results are confirmed by examples. [ABSTRACT FROM AUTHOR]

In this paper some lower and upper estimates of M‐constants for Orlicz–Lorentz function spaces for both, the Luxemburg and the Amemiya norms, are given. Since degenerated Orlicz functions φ and degenerated weighted sequences ω are also admitted, this investigations concern the most possible wide class of Orlicz–Lorentz function spaces. M‐constants were defined in 1969 by E. A. Lifshits, and used by many authors in the study of lattice structures on Banach spaces, as well as in the fixed point theory. [ABSTRACT FROM AUTHOR]