Search

The aim of this paper is to study the existence and uniqueness of periodic solutions for a certain type of nonlinear fractional pantograph differential equation with a ψ -Caputo derivative. The proofs are based on the coincidence degree theory of Mawhin. To show the efficiency of the results, some illustrative examples are included. [ABSTRACT FROM AUTHOR]

We consider a non-instantaneous system represented by a second order nonlinear differential equation in a Banach space E. We use the family of linear bounded operators introduced by Kozak, Darbo fixed point method and Kuratowski measure of noncompactness. A new set of sufficient conditions is formulated which guarantees the existence of the solution of the non-instantaneous system. An example is also discussed to illustrate the efficiency of the obtained results. [ABSTRACT FROM AUTHOR]

This paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section. [ABSTRACT FROM AUTHOR]

We present in this work the existence results and uniqueness of solutions for a class of boundary value problems of terminal type for fractional differential equations with the Hilfer–Katugampola fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Banach contraction principle and Krasnoselskii's fixed point theorem. We illustrate our main findings, with a particular case example included to show the applicability of our outcomes. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for hybrid fractional differential equations involving fractional Caputo derivative of order 1 < α ≤ 2 . Our results rely on a hybrid fixed point theorem for a sum of three operators due to Dhage. An example is provided to illustrate the theory. [ABSTRACT FROM AUTHOR]

This article deals with some existence and uniqueness result of random solutions for some coupled systems of Hilfer and Hilfer–Hadamard fractional differential equations with random effects. Some applications are made of generalizations of classical random fixed point theorems on generalized Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of solutions for a hybrid boundary value problem of Caputo fractional differential equations. The main tool used in our study is associated with the technique of measures of noncompactness. As an application, we give an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, the concept of upper and lower solutions method combined with the fixed point theorem is used to investigate the existence of oscillatory and nonoscillatory solutions for a class of initial value problem for Caputo-Hadamard impulsive fractional differential inclusions. [ABSTRACT FROM AUTHOR]

In this article, we present some existence of weak solutions for a coupled system of implicit fractional differential equations of Hilfer-Hadamard type. Our approach is based on Mönch’s fixed point theorem associated with the technique of measure of weak noncompactness. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to investigate the existence, uniqueness, and Mittag–Leffler–Ulam stability results for a Cauchy problem involving ψ -Caputo fractional derivative with positive constant coefficient in Banach and Fréchet Spaces. The techniques used are a variety of tools for functional analysis. More specifically, we apply Weissinger's fixed point theorem and Banach contraction principle with respect to the Chebyshev and Bielecki norms to obtain the uniqueness of solution on bounded and unbounded domains in a Banach space. However, a new fixed point theorem with respect to Meir–Keeler condensing operators combined with the technique of Hausdorff measure of noncompactness is used to investigate the existence of a solution in Banach spaces. After that, by means of new generalizations of Grönwall's inequality, the Mittag–Leffler–Ulam stability of the proposed problem is studied on a compact interval. Meanwhile, an extension of the well-known Darbo's fixed point theorem in Fréchet spaces associated with the concept of measures of noncompactness is applied to obtain the existence results for the problem at hand. Finally, as applications of the theoretical results, some examples are given to illustrate the feasibility of the main theorems. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of solutions for hybrid fractional differential equations with fractional separated boundary conditions. An existence results is obtained with the use of the technique of measures of noncompactness in the Banach algebras and a fixed point theorem for the product of two operators verifying a Darbo type condition. As application, we give an example to illustrate our results. [ABSTRACT FROM AUTHOR]

This research delves into the field of fractional differential equations with both non-instantaneous impulses and delay within the framework of Banach spaces. Our objective is to establish adequate conditions that ensure the existence, uniqueness, and Ulam–Hyers–Rassias stability results for our problems. The studied problems encompass abstract impulsive fractional differential problems with finite delay, infinite delay, state-dependent finite delay, and state-dependent infinite delay. To provide clarity and depth, we augment our theoretical results with illustrative examples, illustrating the practical implications of our work. [ABSTRACT FROM AUTHOR]

This paper deals with the existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-metric spaces with initial and nonlocal conditions. The arguments are based on some fixed point theorems. Furthermore, two illustrations are presented to demonstrate the plausibility of our results. [ABSTRACT FROM AUTHOR]

This article concerns the existence and Ulam stabilities for a class of random integral equations via Hadamard's fractional integral. Our main tools is a random fixed point theorem with stochastic domain. [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 paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type. [ABSTRACT FROM AUTHOR]

This article studies the existence of solutions and extremal solutions to partial hyperbolic differential equations of fractional order with impulses in Banach algebras under Lipschitz and Carathéodory conditions and certain monotonicity conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the global convergence of successive approximations as well as the uniqueness of the random solution of a coupled random Hilfer fractional differential system. We prove a theorem on the global convergence of successive approximations to the unique solution of our problem. In the last section, we present an illustrative example. [ABSTRACT FROM AUTHOR]

This paper delves into the investigation of existence and uniqueness results concerning the Hilfer–Katugampola random nonlinear fractional differential coupled system within a generalized Banach space. Such problems represent a broadened scope, extending several existing results in the literature and offering potential avenues for furthering the development of this evolving theory. Our findings are derived through the application of various random fixed point theorems, including Banach’s random fixed point theorem, the random nonlinear alternative of the Leray–Schauder type, and Schauder’s random fixed point theorem. To validate our results, an illustrative example is presented in the final section. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with the existence of mild solutions of some impulsive evolution fractional functional differential equations with non-local conditions. The results are obtained by using the Banach contraction principle and Krasnoselski's fixed point theorem combined with the a-Resolvent family. An example is presented to illustrate the main results. [ABSTRACT FROM AUTHOR]