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We aim to investigate the stability property for the certain linear and nonlinear fractional q -difference equations in the Ulam–Hyers and Ulam–Hyers–Rassias sense. To achieve this goal, we prove that three types of the linear q -difference equations of the q -Caputo-like type are Ulam–Hyers stable by using the quantum Laplace transform and quantum Mittag–Leffler function. Moreover, after proving the existence property for a nonlinear Cauchy q -difference initial value problem, we use the same quantum Laplace transform and the q -Gronwall inequality to show that it is generalized Ulam–Hyers–Rassias stable. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of multi-term implicit fractional differential equation with boundary conditions. The application of the Schauder fixed point theorem and the Banach fixed point theorem allows us to establish the criterion for a solution that exists for the given equation, and the solution is unique. Afterwards, we give the criteria of Ulam–Hyers stability and Ulam–Hyers–Rassias stability. Additionally, we present an example to illustrate the practical application and effectiveness of the results. [ABSTRACT FROM AUTHOR]

This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model's intricate dynamics. [ABSTRACT FROM AUTHOR]

In this paper, the existence of a unique solution is established for a coupled system of Langevin fractional problems of ψ -Caputo fractional derivatives with generalized slit-strip-type integral boundary conditions and impulses using the Banach contraction principle. We also find at least one solution to the aforementioned system using some assumptions and Schaefer's fixed point theorem. After that, Ulam–Hyers stability is discussed. Finally, to provide additional support for the main results, pertinent examples are presented. [ABSTRACT FROM AUTHOR]

The aim of this paper is manifold. We first define the new class of operators called MR-Kannan interpolative type contractions, which includes the Kannan, enriched Kannan, interpolative Kannan type, and enriched interpolative Kannan type operators. Secondly, we prove the existence of a unique fixed point for this class of operators. Thirdly, we study Ulam-Hyers stability, well-posedness, and periodic point properties. Finally, an application of the main results to the variational inequality problem is given. [ABSTRACT FROM AUTHOR]

The Ebola virus continues to be the world's biggest cause of mortality, especially in developing countries, despite the availability of safe and effective immunization. In this paper, we construct a fractional-order Ebola virus model to check the dynamical transmission of the disease as it is impacted by immunization, learning, prompt identification, sanitation regulations, isolation, and mobility limitations with a constant proportional Caputo (CPC) operator. The existence and uniqueness of the proposed model's solutions are discussed using the results of fixed-point theory. The stability results for the fractional model are presented using Ulam–Hyers stability principles. This paper assesses the hybrid fractional operator by applying methods to invert proportional Caputo operators, calculate CPC eigenfunctions, and simulate fractional differential equations computationally. The Laplace–Adomian decomposition method is used to simulate a set of fractional differential equations. A sustainable and unique approach is applied to build numerical and analytic solutions to the model that closely satisfy the theoretical approach to the problem. The tools in this model appear to be fairly powerful, capable of generating the theoretical conditions predicted by the Ebola virus model. The analysis-based research given here will aid future analysis and the development of a control strategy to counteract the impact of the Ebola virus in a community. [ABSTRACT FROM AUTHOR]

The human immunodeficiency virus (HIV) causes acquired immunodeficiency syndrome (AIDS), which is a chronic and sometimes fatal illness. HIV reduces an individual's capability against infection and illness by demolishing his or her immunity. This paper presents a new model that governs the dynamical behavior of HIV/AIDS by integrating new compartments, i.e., the treatment class T. The steady-state solutions of the model are investigated, and accordingly, the threshold quantity R 0 is calculated, which describes the global dynamics of the proposed model. It is proved that for R 0 less than one, the infection-free state of the model is globally asymptotically stable. However, as the threshold number increases by one, the endemic equilibrium becomes globally asymptotically stable, and in such case, the disease-free state is unstable. At the end of the paper, the analytic conclusions obtained from the analysis of the ordinary differential equation (ODE) model are supported through numerical simulations. The paper also addresses a comprehensive analysis of a fractional-order HIV model utilizing the Caputo fractional differential operator. The model's qualitative analysis is investigated, and computational modeling is used to examine the system's long-term behavior. The existence/uniqueness of the solution to the model is determined by applying some results from the fixed points of the theory. The stability results for the system are established by incorporating the Ulam–Hyers method. For numerical treatment and simulations, we apply Newton's polynomial and the Toufik–Atangana numerical method. Results demonstrate the effectiveness of the fractional-order approach in capturing the dynamics of the HIV/AIDS epidemic and provide valuable insights for designing effective control strategies. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study nonlinear implicit differential equations with the Caputo–Katugampola fractional derivative. By using Gronwall inequality and Banach fixed-point theorem, the existence of the solution of the implicit equation is proved, and the relevant conclusions about the stability of Ulam–Hyers are obtained. Finally, the correctness of the conclusions is verified by an example. [ABSTRACT FROM AUTHOR]

Here, we shall introduce the new notion of C * -algebra valued bipolar b-metric spaces as a generalization of usual metric spaces, C * -algebra valued metric space, b-metric spaces. In the above-mentioned spaces, we shall define (α A − ψ A) contractions and prove some fixed point theorems for these contractions. Some existing results from the literature are also proved by using our main results. As an application Ulam–Hyers stability and well-posedness of fixed point problems are also discussed. Some examples are also given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this article, Euler's technique was employed to solve the novel post-pandemic sector-based investment mathematical model. The solution was established within the framework of the new generalized Caputo-type fractional derivative for the system under consideration that serves as an example of the investment model. The mathematical investment model consists of a system of four fractional-order nonlinear differential equations of the generalized Liouville–Caputo type. Moreover, the existence and uniqueness of solutions for the above fractional order model under pandemic situations were investigated using the well-known Schauder and Banach fixed-point theorem technique. The stability analysis in the context of Ulam—Hyers and generalized Ulam—Hyers criteria was also discussed. Using the investment model under consideration, a new analysis was conducted. Figures that depict the behavior of the classes of the projected model were used to discuss the obtained results. The demonstrated results of the employed technique are extremely emphatic and simple to apply to the system of non-linear equations. When a generalized Liouville–Caputo fractional derivative parameter (ρ) is changed, the results are asymmetric. The current work can attest to the novel generalized Caputo-type fractional operator's suitability for use in mathematical epidemiology and real-world problems towards the future pandemic circumstances. [ABSTRACT FROM AUTHOR]

The goal of this work is to study a multi-term boundary value problem (BVP) for fractional differential equations in the variable exponent Lebesgue space ( L p (·) ). Both the existence, uniqueness, and the stability in the sense of Ulam–Hyers are established. Our results are obtained using two fixed-point theorems, then illustrating the results with a comprehensive example. [ABSTRACT FROM AUTHOR]

In this article, a new kind of bilateral symmetric additive type functional equation is introduced. One of the interesting characteristics of the equation is the fact that it is ideal for investigating the Ulam–Hyers stabilities in two prominent normed spaces, namely fuzzy and random normed spaces simultaneously. This article analyzes the proposed equation in both spaces. The solution of this equation exhibits the property of symmetry, that is, the left of the object becomes the right of the image, and vice versa. Additionally, the stability results of this functional equation are determined in fuzzy and random normed spaces using direct and fixed point methods. [ABSTRACT FROM AUTHOR]

We present a Caputo fractional order mathematical model that describes the cellular infection of the Hepatitis B virus and the immune response of the body with Holling type II functional response. We study the existence of unique positive solutions and the local and global stability of virus-free and endemic equilibria. Finally, we present numerical results using the Adam-type predictor–corrector iterative scheme. [ABSTRACT FROM AUTHOR]

This article deals with a class of nonlinear fractional differential equations, with initial conditions, involving the Riemann–Liouville fractional derivative of order α ∈ (1 , 2) . The main objectives are to obtain conditions for the existence and uniqueness of solutions (within appropriate spaces), and to analyze the stabilities of Ulam–Hyers and Ulam–Hyers–Rassias types. In fact, different conditions for the existence and uniqueness of solutions are obtained based on the analysis of an associated class of fractional integral equations and distinct fixed-point arguments. Additionally, using a Bielecki-type metric and some additional contractive arguments, conditions are also obtained to guarantee Ulam–Hyers and Ulam–Hyers–Rassias stabilities for the problems under analysis. Examples are also included to illustrate the theory. [ABSTRACT FROM AUTHOR]

This paper is devoted to boundary-value problems for Riemann–Liouville-type fractional differential equations of variable order involving finite delays. The existence of solutions is first studied using a Darbo's fixed-point theorem and the Kuratowski measure of noncompactness. Secondly, the Ulam–Hyers stability criteria are examined. All of the results in this study are established with the help of generalized intervals and piecewise constant functions. We convert the Riemann–Liouville fractional variable-order problem to equivalent standard Riemann–Liouville problems of fractional-constant orders. Finally, two examples are constructed to illustrate the validity of the observed results. [ABSTRACT FROM AUTHOR]

Through literature retrieval and classification, it can be found that for the fractional delay impulse differential system, the existence and uniqueness of the solution and UHR stability of the fractional delay impulse differential system are rarely studied by using the polynomial function of the fractional delay impulse matrix. In this paper, we firstly introduce a new concept of impulsive delayed Mittag–Leffler type solution vector function, which helps us to construct a representation of an exact solution for the linear impulsive fractional differential delay equations (IFDDEs). Secondly, by using Banach's and Schauder's fixed point theorems, we derive some sufficient conditions to guarantee the existence and uniqueness of solutions of nonlinear IFDDEs. Finally, we obtain the Ulam–Hyers stability (UHs) and Ulam–Hyers–Rassias stability (UHRs) for a class of nonlinear IFDDEs. [ABSTRACT FROM AUTHOR]

In this article, we study a system of Hilfer ( k , ψ )-fractional differential equations, subject to nonlocal boundary conditions involving Hilfer ( k , ψ )-derivatives and ( k , ψ )-integrals. The results for the mentioned system are established by using Mönch's fixed point theorem, then the Ulam–Hyers technique is used to verify the stability of the solution for the proposed system. In general, symmetry and fractional differential equations are related to each other. When a generalized Hilfer fractional derivative is modified, asymmetric results are obtained. This study concludes with an applied example illustrating the existence results obtained by Mönch's theorem. [ABSTRACT FROM AUTHOR]

In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions are studied, and new existence and uniqueness results are established in the form of two fixed point theorems. In addition, Ulam–Hyers stability sufficient conditions are proved illustrating the suitability of the derived fundamental results. The obtained results are supported also by an example. Finally, the conclusion notes are highlighted. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and stability results for the (ρ k , ϕ k) -Hilfer fractional integro-differential equations under instantaneous impulse with non-local multi-point fractional integral boundary conditions. We achieve the formulation of the solution to the (ρ k , ϕ k) -Hilfer fractional differential equation with constant coefficients in term of the Mittag–Leffler kernel. The uniqueness result is proved by applying Banach's fixed point theory with the Mittag–Leffler properties, and the existence result is derived by using a fixed point theorem due to O'Regan. Furthermore, Ulam–Hyers stability and Ulam–Hyers–Rassias stability results are demonstrated via the non-linear functional analysis method. In addition, numerical examples are designed to demonstrate the application of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the study of the implicit FDE involving Stieltjes integral boundary conditions. We first exploit some sufficient conditions to guarantee the existence and uniqueness of solutions for the above problems based on the Banach contraction principle and Schaefer's fixed point theorem. Then, we present different kinds of stability such as UHS , GUHS , UHRS , and GUHRS by employing the classical techniques. In the end, the main results are demonstrated by two examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider several problems related to the so-called multi-valued Feng–Liu–Subrahmanyan contractions in complete metric spaces. Existence of the fixed points and of the strict fixed points, as well as data dependence and stability properties for the fixed point problem, are discussed. Some results are presented, under appropriate conditions, and some open questions are pointed out. Our results extend recent results given for multi-valued graph contractions and multi-valued Subrahmanyan contractions. [ABSTRACT FROM AUTHOR]

In the current paper, we analyzed the existence and uniqueness of a solution for a coupled system of impulsive hybrid fractional differential equations involving ψ -Caputo fractional derivatives with generalized slit-strips-type integral boundary conditions. We also study the Ulam–Hyers stability for the considered system. For the existence and uniqueness of the solution, we use the Banach contraction principle. With the help of Schaefer's fixed-point theorem and some assumptions, we also obtain at least one solution of the mentioned system. Finally, the main results are verified with an appropriate example. [ABSTRACT FROM AUTHOR]

The subject of this paper is the existence, uniqueness and stability of solutions for a new sequential Van der Pol–Duffing (VdPD) jerk fractional differential oscillator with Caputo–Hadamard derivatives. The arguments are based upon the Banach contraction principle, Krasnoselskii fixed-point theorem and Ulam–Hyers stabilities. As applications, one illustrative example is included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this work, we replaced the integer derivative with Caputo derivative to model the transmission dynamics of measles in an epidemic situation. We began by recalling some results on the local and global stability of the measles-free equilibrium point as well as the local stability of the endemic equilibrium point. We computed the basic reproduction number of the fractional model and found that is it equal to the one in the integer model when the fractional order ν = 1. We then performed a sensitivity analysis using the global method. Indeed, we computed the partial rank correlation coefficient (PRCC) between each model parameter and the basic reproduction number R0 as well as each variable state. We then demonstrated that the fractional model admits a unique solution and that it is globally stable using the Ulam–Hyers stability criterion. Simulations using the Adams-type predictor–corrector iterative scheme were conducted to validate our theoretical results and to see the impact of the variation of the fractional order on the quantitative disease dynamics. [ABSTRACT FROM AUTHOR]

This article discusses several forms of Ulam stability of nonlinear fractional delay differential equations. Our investigation is based on a generalised Gronwall's inequality and Picard operator theory. Implementations are provided to demonstrate the stability results obtained for finite intervals. [ABSTRACT FROM AUTHOR]

In this manuscript we introduce a quadratic integral equation of the Urysohn type of fractional variable order. The existence and uniqueness of solutions of the proposed fractional model are studied by transforming it into an integral equation of fractional constant order. The obtained new results are based on the Schauder's fixed-point theorem and the Banach contraction principle with the help of piece-wise constant functions. Although the used methods are very powerful, they are not applied to the quadratic integral equation of the Urysohn type of fractional variable order. With this research we extend the applicability of these techniques to the introduced the Urysohn type model of fractional variable order. The applicability of the new results are demonstrated by providing Ulam–Hyers stability criteria and an example. Moreover, the presented results lead to future progress and expansion of the theory of fractional-order models, as well as of the concept of entropy in the framework of fractional calculus. Further, an example is constructed to demonstrate the reasonableness and effectiveness of the observed results. [ABSTRACT FROM AUTHOR]

In the context of a complete metric space, we will consider the common fixed point problem for two self operators. The operators are assumed to satisfy a general contraction type condition inspired by the Ćirić fixed point theorems. Under some appropriate conditions we establish existence, uniqueness and approximation results for the common fixed point. In the same framework, the second problem is to study various stability properties. More precisely, we will obtain sufficient conditions assuring that the common fixed point problem is well-posed and has the Ulam–Hyers stability, as well as the Ostrowski property for the considered problem. Some examples and applications are finally given in order to illustrate the abstract theorems proposed in the first part of the paper. Our results extend and complement some theorems in the recent literature. [ABSTRACT FROM AUTHOR]

In this work, we introduce a mixed type of quadratic-additive (QA) functional equation and obtain its general solution. The objective of this work is to investigate the Ulam–Hyers stability of this quadratic-additive (QA) functional equation in matrix paranormed spaces (briefly, MP spaces) using the Hyers method for the factor sum of norms. [ABSTRACT FROM AUTHOR]

In this article, we investigate sufficient conditions for the existence and stability of solutions to a coupled system of ψ -Caputo hybrid fractional derivatives of order 1 < υ ≤ 2 subjected to Dirichlet boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of the Leray–Schauder alternative theorem and Banach's contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam–Hyers. Finally, we provide one example in order to show the validity of our results. [ABSTRACT FROM AUTHOR]

The purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability of solutions to a coupled system of fractional differential equations with Erdélyi–Kober and Riemann–Liouville integral boundary conditions. The Banach fixed point theorem is used to prove the uniqueness of solutions, while the Leray–Schauder alternative is used to prove the existence of solutions. Furthermore, we conclude that the solution to the discussed problem is Hyers–Ulam stable. The results are illustrated with examples. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) of solutions of a nonlinear neutral stochastic fractional differential system. We prove the existence and uniqueness of solutions to the proposed system by using fixed point theorems and the Banach contraction principle. Also, by using fundamental schemes of fractional calculus, we study the (U-Hs) to the solutions of our suggested system. Besides, we study an example, best describing our main result. [ABSTRACT FROM AUTHOR]

Applications and modeling of various phenomena in all areas of scientific research require finding numerical solutions for differential, partial differential, integral, or integro-differential equations. In addition to proving theoretical convergence and giving error estimates, stability of numerical methods for such operator equations is a fundamental property that it is necessary for the method to produce a valid solution. This Special Issue focuses on new theoretical and numerical studies concerning the techniques used for proving stability or instability of numerical schemes, which extend or improve known results. It also includes applications to non-linear physical, chemical, and engineering systems, arising in dynamics of waves, diffusion, or transport problems. [ABSTRACT FROM AUTHOR]

Few papers have been published to date regarding the stability of neural networks described by fractional difference operators. This paper makes a contribution to the topic by presenting a variable-order fractional discrete neural network model and by proving its Ulam–Hyers stability. In particular, two novel theorems are illustrated, one regarding the existence of the solution for the proposed variable-order network and the other regarding its Ulam–Hyers stability. Finally, numerical simulations of three-dimensional and two-dimensional variable-order fractional neural networks were carried out to highlight the effectiveness of the conceived theoretical approach. [ABSTRACT FROM AUTHOR]

In the theory of differential equations, the study of existence and the uniqueness of the solutions are important. In the last few decades, many researchers have had a keen interest in finding the existence–uniqueness solution of constant fractional differential equations, but literature focusing on variable order is limited. In this article, we consider a Caputo type variable order fractional differential equation. First, we present the existence–uniqueness of a solution of the considered problem. Secondly, By borrowing the idea from the theory of ordinary differential equations, we extend the continuation theorem for the variable order fractional differential equation. Further, we prove the global existence results. Finally, we present different types of Ulam–Hyers stability results, which have never been studied before for the Caputo type variable order fractional differential equation. [ABSTRACT FROM AUTHOR]

In this paper we study Hyers-Ulam stability of Euler's equation in the calculus of variations in two special cases: when F = F (x , y ′) and when F = F (y , y ′). For the first case we use the direct method and for the second case we use the Laplace transform. In the first Theorem and in the first Example the corresponding estimations for J y x − J y 0 x are given. We mention that it is the first time that the problem of Ulam-stability of extremals for functionals represented in integral form is studied. [ABSTRACT FROM AUTHOR]

This paper investigates existence, uniqueness, and Ulam's stability results for a nonlinear implicit ψ -Hilfer FBVP describing Navier model with NIBC s. By Banach's fixed point theorem, the unique property is established. Meanwhile, existence results are proved by using the fixed point theory of Leray-Schauder's and Krasnoselskii's types. In addition, Ulam's stability results are analyzed. Furthermore, several instances are provided to demonstrate the efficacy of the main results. [ABSTRACT FROM AUTHOR]

Fractional-order boundary value problems are used to model certain phenomena in chemistry, physics, biology, and engineering. However, some of these models do not meet the existence and uniqueness required in the mainstream of mathematical processes. Therefore, in this paper, the existence, stability, and uniqueness for the solution of the coupled system of the Caputo-type sequential fractional differential equation, involving integral boundary conditions, was discussed, and investigated. Leray–Schauder's alternative was applied to derive the existence of the solution, while Banach's contraction principle was used to examine the uniqueness of the solution. Moreover, Ulam–Hyers stability of the presented system was investigated. It was found that the theoretical-related aspects (existence, uniqueness, and stability) that were examined for the governing system were satisfactory. Finally, an example was given to illustrate and examine certain related aspects. [ABSTRACT FROM AUTHOR]

In this paper, we establish sufficient conditions to approve the existence and uniqueness of solutions of a nonlinear implicit ψ -Hilfer fractional boundary value problem of the cantilever beam model with nonlinear boundary conditions. By using Banach's fixed point theorem, the uniqueness result is proved. Meanwhile, the existence result is obtained by applying the fixed point theorem of Schaefer. Apart from this, we utilize the arguments related to the nonlinear functional analysis technique to analyze a variety of Ulam's stability of the proposed problem. Finally, three numerical examples are presented to indicate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This article introduces a new type of C * -algebra valued modular G-metric spaces that is more general than both C * -algebra valued modular metric spaces and modular G-metric spaces. Some properties are also discussed with examples. A few common fixed point results in C * -algebra valued modular G-metric spaces are discussed using the " C * -class function", along with some suitable examples to validate the results. Ulam–Hyers stability is used to check the stability of some fixed point results. As applications, the existence and uniqueness of solutions for a particular problem in dynamical programming and a system of nonlinear integral equations are provided. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the class of enriched multivalued contraction mappings. Both single-valued and multivalued enriched contractions are defined by means of symmetric inequalities. Our main result extends and generalizes the recent result of Berinde and Păcurar (Approximating fixed points of enriched contractions in Banach spaces, Journal of Fixed Point Theory and Applications, 22 (2), 1–10, 2020). We also study a data dependence problem of the fixed point set and Ulam–Hyers stability of the fixed point problem for enriched multivalued contraction mappings. Applications of the results obtained to the problem of the existence of a solution of differential inclusions and dynamic programming are presented. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of implicit-type coupled system with integral boundary conditions involving Caputo fractional derivatives. First, the existence result of solutions for the considered system is obtained by means of topological degree theory. Next, Ulam–Hyers stability and generalized Ulam–Hyers stability are studied under some suitable assumptions. Finally, one example is worked out to illustrate the main results. [ABSTRACT FROM AUTHOR]

Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result regarding a Ulam–Hyers stability result for the corresponding fixed point problem. [ABSTRACT FROM AUTHOR]

A delayed perturbation of the Mittag-Leffler type matrix function with logarithm is proposed. This combines the classic Mittag–Leffler type matrix function with a logarithm and delayed Mittag–Leffler type matrix function. With the help of this introduced delayed perturbation of the Mittag–Leffler type matrix function with a logarithm, we provide an explicit form for solutions to non-homogeneous Hadamard-type fractional time-delay linear differential equations. We also examine the existence, uniqueness, and Ulam–Hyers stability of Hadamard-type fractional time-delay nonlinear equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov's sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy–Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam–Hyers stability of the fixed point problem. An example is also given to sustain the presented results. [ABSTRACT FROM AUTHOR]

In this paper, by using the Banach contraction principle and the Schauder's fixed point theorem, we investigate existence results for a fractional impulsive sum-difference equations with periodic boundary conditions. Moreover, we also establish different kinds of Ulam stability for this problem. An example is also constructed to demonstrate the importance of these results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov's sense under a contractive condition of Hardy–Rogers type. The data dependence of the fixed point set, the well-posedness of the fixed point problem and the Ulam–Hyers stability are also studied. [ABSTRACT FROM AUTHOR]