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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, we study the generalized concept of q-calculus with respect to another function. The ψ-quantum Riemann-Liouville fractional integral, ψ-quantum Riemann-Liouville fractional derivative, and ψ-quantum Caputo fractional derivative were introduced. The existence, uniqueness, and Ulam-Hyers stability of the solutions with the mentioned derivatives were established. Finally, some examples are considered to demonstrate the results obtained. [ABSTRACT FROM AUTHOR]

The analysis of stability in functional equations (FEs) within neutrosophic normed spaces is a significant challenge due to the inherent uncertainties and complexities involved. This paper proposes a novel approach to address this challenge, offering a comprehensive framework for investigating stability properties in such contexts. Neutrosophic normed spaces are a generalization of traditional normed spaces that incorporate neutrosophic logic. By providing a systematic methodology for addressing stability concerns in neutrosophic normed spaces, our approach facilitates enhanced understanding and control of complex systems characterized by indeterminacy and uncertainty. The primary focus of this research is to propose a novel class of Euler-Lagrange additive FE and investigate its Ulam-Hyers stability in neutrosophic normed spaces. Direct and fixed point techniques are utilized to achieve the required results. [ABSTRACT FROM AUTHOR]

In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class. We analyze the dynamics of the alcohol addiction model for the first time using advanced operators known as fractal–fractional operators, which incorporate two distinct fractal and fractional orders with the well-known Caputo derivative based on power law kernels. The existence and uniqueness of the newly developed fractal–fractional alcohol addiction model are shown using the Picard–Lindelöf and fixed point theories. Initially, a comprehensive qualitative analysis of the alcohol addiction fractional model is presented. The possible equilibria of the model and the threshold parameter called the reproduction number are evaluated theoretically and numerically. The boundedness and biologically feasible region for the model are derived. To assess the stability of the proposed model, the Ulam–Hyers coupled with the Ulam–Hyers–Rassias stability criteria are employed. Moreover, utilizing effecting numerical schemes, the models are solved numerically and a detailed simulation and discussion are presented. The model global dynamics are shown graphically for various values of fractional and fractal dimensions. The present study aims to provide valuable insights for the understanding the dynamics and control of alcohol addiction within a community. [ABSTRACT FROM AUTHOR]

In this work, we analyze a q-fractional jerk problem having anti-periodic boundary conditions. The focus is on investigating whether a unique solution exists and remains stable under specific conditions. To prove the uniqueness of the solution, we employ a Banach fixed point theorem and a mathematical tool for establishing the presence of distinct fixed points. To demonstrate the availability of a solution, we utilize Leray–Schauder's alternative, a method commonly employed in mathematical analysis. Furthermore, we examine and introduce different kinds of stability concepts for the given problem. In conclusion, we present several examples to illustrate and validate the outcomes of our study. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two types of weak enriched contractions, namely weak enriched F -contraction, weak enriched F ′ -contraction, and k-fold averaged mapping based on Kirk's iterative algorithm of order k. The types of contractions introduced herein unify, extend, and generalize several existing classes of enriched and weak enriched contraction mappings. Moreover, K-fold averaged mappings can be viewed as a generalization of the averaged mappings and double averaged mappings. We then prove the existence of a unique fixed point of the k-fold averaged mapping associated with weak enriched contractions introduced herein. We study necessary conditions that guarantee the equality of the sets of fixed points of the k-fold averaged mapping and weak enriched contractions. We show that an appropriate Kirk's iterative algorithm can be used to approximate a fixed point of a k-fold averaged mapping and of the two weak enriched contractions. We also study the well-posedness, limit shadowing property, and Ulam–Hyers stability of the k-fold averaged mapping. We provide necessary conditions that ensure the periodic point property of each illustrated weak enriched contraction. Some examples are presented to show that our results are a potential generalization of the comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

The primary aim of this paper is to focus on the stability analysis of an advanced neural stochastic functional differential equation with finite delay driven by a fractional Brownian motion in a Hilbert space. We examine the existence and uniqueness of mild solution of d x a (s) + g (s , x a (s - ω (s))) = I x a (s) + f (s , x a (s - ϱ (s))) d s + ς (s) d ϖ H (s) , 0 ≤ s ≤ T , x a (s) = ζ (s) , - ρ ≤ s ≤ 0. The main goal of this paper is to investigate the Ulam–Hyers stability of the considered equation. We have also provided numerical examples to illustrate the obtained results. This article also discusses the Euler–Maruyama numerical method through two examples. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate the existence and uniqueness of solution for the Darboux problem with modified argument on both bounded and unbounded domains. Then, we derive different types of the Ulam stability for the proposed problem on these domains. Finally, we present some illustrative examples to support our results. [ABSTRACT FROM AUTHOR]

In this paper, by applying fractional quantum calculus, we study a nonlinear Duffing-type equation with three sequential fractional q-derivatives. We prove the existence and uniqueness results by using standard fixed-point theorems (Banach and Schaefer fixed-point theorems). We also discuss the Ulam–Hyers and the Ulam–Hyers–Rassias stabilities of the mentioned Duffing problem. Finally, we present an illustrative example and nice application; a Duffing-type oscillator equation with regard to our outcomes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalizations of the concept of MR-Kannan type contractions and utilize those conditions to derive new fixed point theorems under both contractive and non-contractive conditions. Our approach enhances various existing results related to enriched mappings. [ABSTRACT FROM AUTHOR]

This study is motivated through the interesting non-Arcchimedean stability results of ρ-inequalities and ρ-equations arising from linear, second power, third power and fourth power mappings. The aim of this paper is to determine the solutions of new multiplicative inverse µ-inequalities and µ-equations arising from multiplicative inverse mapping. Further, their stabilities involved with various superior limits are proved in the context of non-Archimedean complete normed spaces. [ABSTRACT FROM AUTHOR]

Fish farming, a potential activity for the production of protein with high nutritional value, has emerged as a substantial source of income in the modern world. The degradation of natural materials uses oxygen to reduce them below the life-support stage. A huge area with an excessive amount of water swamp for oxygen exchange makes for the ideal ecosphere for fish farming, yet the mussel population may grow swiftly in a really modest water swapping farm producing a lot of feed. In this study, we examine the dynamics and chaotic behavior of a fish farm model containing populations of nutrients and mussels with different kernels insight of fractal-fractional operator. We examined the positively invariant area as well as demonstrate positive, bounded solutions of the model. We also show the equilibrium states for the occurrence and extinction of species. We prove the existence and uniqueness of positive solutions through fixed-point theorems and verified the Ulam–Hyers stability for proposed model. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version for the various kernels, which include the power-law and Mittag–Leffler kernel. We develop some numerical simulations to test our theoretical conclusions with chaotic behavior at different fractional-order values. [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]

Recently, numerous demonstrative investigations on the mathematical modelling and analysis of Covid-19 have been performed. In this regard, a mathematical model is introduced to demonstrate the effects of vaccination on Covid-19. This study presents the five compartmental groups of the model, namely susceptible, infected, exposed, recovered groups, and vaccinated people. To make the model more realistic, the existing integer-order system has been modified using the Mittag–Leffler kernel. The formation of a fractional-order model shows the validity of this generalization with memory. In addition to the positivity solution, existence, uniqueness, and biologically feasible region are considered. The Ulam–Hyers stability is established through fixed-point theory and nonlinear analysis. The basic reproduction number, which means the number of people predicted to be secondarily infected among the susceptible population, is calculated. The considered model is assessed by using the Atangana–Baleanu fractional operator, and the fractional Adams–Bashforth numerical technique based on Lagrange polynomial interpolation is adopted to solve the model. Further, the error analysis of the present method has also been included. The behaviour of the solution is demonstrated through numerical simulations with the help of graphical representations. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the new concept of an impulsive delayed vector function, which helps us to build the representation of an exact solution for the linear impulsive oscillating differential delay systems (IODDSs). Second, we derive some sufficient conditions to guarantee the existence and uniqueness of solution by Schauder's and Banach's fixed point theorems for a new class of nonlinear IODDSs. Finally, we obtain the Ulam‐Hyers stability (UHs) and Ulam‐Hyers‐Rassias stability (UHRs) for nonlinear IODDSs, and two examples are presented to illustrate the main results of our study. [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]

This paper is devoted to the study of the dynamical behavior of the tritrophic interaction amongst plants, herbivores and carnivores mathematical model, expressed by three nonlinear ordinary differential equations under fractal–fractional derivative in the Caputo sense. We use fixed point theory to ensure that one solution exists to the proposed model. In addition, Hyers–Ulam's stability analysis is studied by using theorem of functional analysis. For the numerical solution, we apply the fractional Adams–Bashforth iterative technique. For arbitrary fractional order and fractal dimensions, we study the dynamical and chaotic behavior of the obtained results for the considered model. Using Matlab 16, the system is then solved to get the required numerical solution for the proposed system. From the numerical simulations, we observed that the decay in fractional order dynamics of the system is stabilized when the amplitude of the oscillations becomes smaller. [ABSTRACT FROM AUTHOR]

In this article, we study the existence and uniqueness along with Ulam‐type stability of fractional integro causal evolution impulsive systems on time scales. To establish our main results, we use Picard operator along with abstract Grönwall inequality and Gröwall lemma. We constitute some assertions to remove difficulties. At the end, the results are demonstrated via the support of an example. [ABSTRACT FROM AUTHOR]

This article is devoted to prove the existence and uniqueness (EU) of solution of fractional Itô–Doob stochastic differential equations (FIDSDE) with order ϰ∈(0,1)$$ \mathrm{\varkappa}\in \left(0,1\right) $$ by using the fixed point technique (FPT). We analyze the Ulam–Hyers stability (UHS) of FIDSDE by using the Gronwall inequality (GI) and the stochastic analysis techniques. We present an application of our results by two theoretical examples. [ABSTRACT FROM AUTHOR]

Recently, many studies on fractional coupled systems involving different sequential fractional derivatives have appeared during the past several years. The paper is dealing with a coupled system of three sequential Caputo fractional differential equations, and the designed system absorbs none of the commutativity and the semigroup properties. The Banach contraction principle is used for proving the existence and uniqueness results. We prove the existence of at least one is obtained by using the Leray–Schauder alternative. The Ulam–Hyers–Rassias stability of the considered system is defined and discussed. An illustrative example is also presented. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study properties of Ξ-Hilfer fuzzy fractional differential equations which are useful in modeling a variety of phenomena in physical sciences. The existence, uniqueness and stability of solutions are obtained. The technique used for study is the fixed point theorem and Gronwall inequality. Ulam-Hyers-Rassias stability of the solution is also investigated. [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 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]

Abstract The developed article considers SIR problems for the recent COVID-19 pandemic, in which each component is divided into two subgroups: young and adults. These subgroups are distributed among two classes in each compartment, and the effect of COVID-19 is observed in each class. The fractional problem is investigated using the non-singular operator of Atangana Baleanu in the Caputo sense (ABC). The existence and uniqueness of the solution are calculated using the fundamental theorems of fixed point theory. The stability development is also determined using the Ulam-Hyers stability technique. The approximate solution is evaluated using the fractional Adams-Bashforth technique, providing a wide range of choices for selecting fractional order parameters. The simulation is plotted against available data to verify the obtained scheme. Different fractional-order approximations are compared to integer-order curves of various orders. Therefore, this analysis represents the recent COVID-19 pandemic, differentiated by age at different fractional orders. The analysis reveals the impact of COVID-19 on young and adult populations. Adults, who typically have weaker immune systems, are more susceptible to infection compared to young people. Similarly, recovery from infection is higher among young infected individuals compared to infected cases in adults. [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]

In this paper, by applying Pachpatte's type integral inequality with integral impulses, we investigate Ulam–Hyers and Ulam–Hyers–Rassias stabilities for the impulsive Volterra delay integrodifferential equation Banach spaces. Suitable examples are given to support the obtained results. [ABSTRACT FROM AUTHOR]

Discrete tempered fractional calculus, as a fresh generalization of discrete fractional calculus, takes both the advantages of discrete fractional calculus and its tempered fractional counterpart, which has great potential value in the interpretation of special physical phenomena. However, its essential characteristics are far from clarifying. Meanwhile, the primary goal of this study is to enrich the vital characteristics of discrete tempered fractional calculus in the presence of required domains for diverse scenarios. First, the reciprocal properties of the tempered fractional summation and difference operators, as well as the discrete version of Taylor's formula, are established. The formulae of the discrete Laplace transform for discrete tempered fractional calculus are also determined with the aid of discrete convolution. Then, the well-posedness of tempered fractional difference equation is investigated, along with the exploration on the corresponding Volterra summation equation, and the existence, uniqueness and continuous dependence as well. In the aspect of application, the criterion of Ulam–Hyers stability of tempered fractional difference equation on finite time interval is obtained in light of a novel discrete Gronwall inequality. Besides, all examples are showed to verify the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

In this study, we proposed a novel approach for modeling the dynamics of a three-agent financial bubble using the fractal-fractional (FF) derivative of the Caputo sense. This new concept was developed to deal with the complex geometry of any dynamical system, and it utilizes both the fractional derivative for the order and the fractal term for the order of the independent variables. The model was investigated using the conformable order derivative of the Caputo operator, with a focus on the fractal dimension and fractional order. The existence and uniqueness of the solution were tested using a FF global derivative, and the approximate root of the system was calculated using the numerically iterative technique of the Newton polynomial. To verify the accuracy of the approximate root scheme, we applied the power singular law with two fractional parameters in the developed numerical technique. The curve representation of the system was also verified by applying the data for the fractals and different conformable orders. Additionally, we tested the sensitivities of the fractional parameters and dynamical system parameters by varying the parameter values. This allowed us to gain a better understanding of how changes in these parameters affect the system's behavior and stability. As a result, this study presents an innovative and effective approach for modeling the dynamics of financial bubbles using the FF derivative of the Caputo sense. The results of this research contribute to the ongoing efforts to develop more accurate and comprehensive models of complex systems in economics and finance. [ABSTRACT FROM AUTHOR]

Our main objectives in the paper are to investigate the existence and uniqueness of solution for a class of implicit fractional‐order boundary value problem with Riemann–Liouville derivative via generalized boundary conditions. Furthermore, different kinds of Ulam stability are discussed. By giving a few examples, the key findings are demonstrated. [ABSTRACT FROM AUTHOR]

In the present paper, first, a ψ$$ \psi $$‐delayed Mittag–Leffler type function is introduced, which generalizes the existing delayed Mittag–Leffler type function. Second, by means of ψ$$ \psi $$‐delayed Mittag–Leffler type function, an exact analytical solution formula to non‐homogeneous linear delayed Langevin equations involving two distinct ψ$$ \psi $$‐Caputo type fractional derivatives of general orders is obtained. Moreover, existence and uniqueness, stability of solution to nonlinear delayed Langevin fractional differential equations is obtained in the weighted space. Numerical and simulated examples are shared to exemplify the theoretical findings. [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]

This paper deals with a nonlinear hybrid differential equation written using a fractional derivative with a Mittag–Leffler kernel. Firstly, we establish the existence of solutions to the studied problem by using the Banach contraction theorem. Then, by means of the Dhage fixed‐point principle, we discuss the existence of mild solutions. Finally, we study the Ulam–Hyers stability of the introduced fractional hybrid problem. [ABSTRACT FROM AUTHOR]

In this paper, we discussed the existence, uniqueness and Ulam-type stability of solutions for sequential coupled hybrid fractional differential equations with two derivatives. The uniqueness of solutions is established by means of Banach's contraction mapping principle, while the existence of solutions is derived from Leray-Schauder's alternative fixed point theorem. Further, the Ulam-type stability of the addressed problem is studied. Finally, an example is provided to check the validity of our obtained 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]

This research inscription gets to grips with two novel varieties of boundary value problems. One of them is a hybrid Langevin fractional differential equation, whilst the other is a coupled system of hybrid Langevin differential equation encapsuling a collective fractional derivative known as the ψ-Caputo fractional operator. Such operators are generated by iterating a local integral of a function with respect to another increasing positive function Ψ. The existence of the solutions of the aforehand equations is tackled by using the Dhage fixed point theorem, whereas their uniqueness is handled using the Banach fixed point theorem. On the top of this, the stability within the scope of Ulam–Hyers of solutions to these systems are also considered. Two pertinent examples are presented to corroborate the reported results. [ABSTRACT FROM AUTHOR]

This primer article focuses on the existence, uniqueness and Ulams stability of semilinear nonautonomous dynamic problem with impulses on time scales, by utilizing fixed point method. We establish our results with the help of abstract Grönwall inequality and Picard operator. We utilize some assertions to overcome difficulties. To demonstrate our main result, we provide an example at the end. [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]

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]

In this manuscript, the existence, uniqueness, and stability of solutions to the terminal value problem of Riemann‐Liouville fractional equations are established in the variable exponent Lebesgue spaces Lp(.)$$ {L}^{p(.)} $$. We convert the variable exponent Lebesgue spaces Lp(.)$$ {L}^{p(.)} $$ to the Lebesgue spaces using the generalized intervals and piece‐wise constant function. Further, the Banach contraction principle is used, the Ulam‐Hyers‐stability is examined, and finally, we construct an example. [ABSTRACT FROM AUTHOR]

For finite-dimensional linear differential systems with bounded coefficients we prove that their exponential dichotomy on R is equivalent to their Ulam-Hyers stability on R with uniqueness. We also consider abstract non-autonomous evolution equations which are exponentially bounded and exponentially dichotomic and prove that Ulam-Hyers stability with uniqueness is maintained when perturbing them with a nonlinear term having a sufficiently small Lipschitz constant. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the class of R-enriched interpolative Kannan pair and proved a common fixed point result in the context of R-complete convex metric spaces. Some examples are presented to support the concepts introduced herein. Moreover, we study the well-posedness, limit shadowing property and Ulam-Hyers stability of the mappings introduced herein. Our result extend and generalize several comparable results in the existing literature. [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]

In this work, we investigate two types of boundary value problems for a system of coupled Atangana–Baleanu-type fractional differential equations with nonlocal boundary conditions. The fractional derivatives are applied to serve as a nonlocal and nonsingular kernel. The existence and uniqueness of solutions for proposed problems using Krasnoselskii's and Banach's fixed-point approaches are established. Moreover, nonlinear analysis is used to build the Ulam–Hyers stability theory. Subsequently, we discuss two compelling examples to demonstrate the utility of our study. [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]