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This paper deals with some existence of solutions for some classes of coupled systems of conformable fractional differential equations with initial and boundary conditions in Banach and Fréchet spaces. Our results are based on some fixed point theorems. Some illustrative examples are presented in the last section. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of mild solution for impulsive fractional inclusions with state-dependent delay in Banach spaces. Our study is based on the nonlinear alternative of Leray-Schauder type for multivalued maps due to Martelli. An example is provided to illustrate the main result.

This study examines if there are any mild solutions for the perturbed partial functional and neutral functional evolution equations with state-dependent delay when the derivative utilizes Caputo's fractional derivative, as well as whether any such solutions are unique. The solution itself determines how long the equations take to solve. The work proves the existence and uniqueness of these solutions using semigroup theory and the Banach contraction theorem in Banach spaces. [ABSTRACT FROM AUTHOR]

This paper explores the existence and stability of implicit neutral Caputo fractional qdifference equations within four distinct classes, incorporating various delay types such as finite, infinite, and state-dependent delays. To establish the existence of solutions, we utilize the fixed point theorem of Krasnoselskii in Banach spaces. The concluding section provides illustrative examples that highlight the obtained results. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of mild solutions of a non-instantaneous integrodi erential equations on unbounded domain via resolvent operators in Banach space. For our proofs, we employ the semigroups theory and Schauder's fixed point theorem. Moreover, we show that solutions of our problem are attractive. Finally, an example is given to validate the theory part. [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]

In the present article, we prove some existence results for a class of implicit Caputo fractional q-difference equations with non instantaneous impulses in Banach spaces. The used techniques rely on the concepts of measure of noncompactness and the use of suitable fixed point theorems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and Ulam stability results for a class of boundary value problems for implicit Riesz-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The result are based on Monch fixed point theorem associated with the technique of measure of noncompactness. An illustrative example is given to validate our main results. [ABSTRACT FROM AUTHOR]

This paper deals with some existence results for a class of implicit fractional q-difference equations. The results are based on the fixed point theory in Banach spaces and the concept of measure of noncompactness. An illustrative example is given in the last section. [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]

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

In this paper, we deal with the existence and uniqueness of solutions of a coupled system of nonlinear implicit fractional differential equations of Caputo-type modification of the Erdélyi-Kober involving both retarded and advanced arguments. The arguments are based upon the Banach contraction principle and Schauder's fixed point theorem. An example is included to show the applicability of our outcomes. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of periodic mild solutions for a class of second order evolution equations with not instantaneous impulses. The techniques used are some fixed point theorems in Banach spaces (Darbo and Kuratowski fixed point theorems), the Poincare operator and the measure of noncompactness. [ABSTRACT FROM AUTHOR]

This article deals with some questions of existence and uniqueness of random solutions for some coupled systems of random Hilfer and Hilfer-Hadamard fractional differential equations with finite delay. We use some generalizations of classical random fixed point theorems on generalized Banach spaces. [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]

This article deals with some results about the existence of solutions and bounded solutions and the attractivity for a class of fractional q-difference equations. Some applications are made of Schauder fixed point theorem in Banach spaces and Darbo fixed point theorem in Fréchet spaces. We use some technics associated with the concept of measure of noncompactness and the diagonalization process. Some illustrative examples are given in the last section. [ABSTRACT FROM AUTHOR]

This paper deals with some existence of mild solutions for two classes of impulsive integrodifferential equations in Banach spaces. Our results are based on the fixed point theory and the concept of measure of noncompactness with the help of the resolvent operator. Two illustrative examples are given in the last section. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some existence and Ulam's type stability concepts for partial fractional random differential inclusions in Banach spaces with a nonconvex valued right hand side. Our existence results are based upon Nowak's fixed point theorem for random multivalued contraction operators. [ABSTRACT FROM AUTHOR]

In this paper, we present some results concerning the existence of weak solutions for some functional Hilfer and Hadamard fractional differential inclusions. The Mönch's fixed point theorem and the concept of measure of weak noncompactness are the main tools used to carry out our results. [ABSTRACT FROM AUTHOR]

We provide some sufficient conditions ensuring the existence of solutions of Caputo type modification of the Erdélyi-Kober fractional differential inclusions in Banach spaces with retarded and advanced arguments. We use Mönch's and Darbo's fixed point theorems and the concept of a measure of noncompactness. As illustration, an example is presented. [ABSTRACT FROM AUTHOR]

This article deals with results concerning the existence of solutions for some functional implicit of Caputo type modification of the Erdélyi-Kober fractional differential equations, with both retarded and advanced arguments. The results are based on the Mönch's and Darbo's fixed point theorem associated with the technique of measure of noncompactness, and we present an illustrative example. [ABSTRACT FROM AUTHOR]

This article focuses on the existence and Ulam–Hyers–Rassias stability outcomes pertaining to a specific category of impulsive integro‐differential inclusions (with instantaneous and non‐instantaneous impulses). These problems are examined using resolvent operators, drawing from the Grimmer perspective. Our analysis is based on Bohnenblust–Karlin's and Darbo's fixed point theorems for multivalued mappings in Banach spaces. Additionally, we provide an illustrative example to reinforce and demonstrate the validity of our findings. [ABSTRACT FROM AUTHOR]

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

In this paper we prove the existence and stability of solutions of a class of Hadamard–Volterra–Stieltjes integral equations in the Banach space of continuous and bounded functions on unbounded interval. That result is proved under rather general hypotheses. The main tools used in our considerations are the concept of measure of noncompactness in conjunction with the Darbo and Mönch fixed point theorems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence mild solutions of second order semilinear evolution equation in Banach space. The results are obtained by using the fixed point technique and Kuratowski measure of noncompactness. We give an example for illustration. [ABSTRACT FROM AUTHOR]

This paper deals with some existence results in Banach spaces for Hilfer and Hilfer-Hadamard fractional differential inclusions. The main tools used in the proofs are Monch's fixed point theorem and the concept of a measure of noncompactness. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of mild solutions for a class of semilinear fractional order integro-differential inclusions with infinite delay in Banach spaces. Sufficient conditions for the existence of solutions are derived by using a nonlinear alternative of Leray–Schauder type for multivalued maps due to Martelli. An example is given to illustrate the theory. [ABSTRACT FROM AUTHOR]

In the present article, we prove some results concerning the existence of solutions for some classes of Hadamard fractional differential equations with instantaneous and noninstantaneous impulses in Banach spaces. The technique relies on the concept of measure of noncompactness and the fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper, we shall present some uniqueness and Ulam's type stability concepts for the Darboux problem of partial functional differential equations with not instantaneous impulses and state-dependent delay in Banach spaces. Some examples are also provided to illustrate our results. [ABSTRACT FROM AUTHOR]

We deal in this paper with some existence results in Banach spaces for some Hilfer and Hadamard differential inclusions of fractional order. The Mönch's fixed point theorem and the concept of measure of noncompactness are the main tools used to carry out our results. [ABSTRACT FROM AUTHOR]

In this paper, we present results concerning the existence of weak solutions for some functional implicit Hilfer fractional differential equations with not instantaneous impulses in Banach spaces. The main results are proved by applyingMönch's fixed point theorem associated with the technique of measure of weak noncompactness, and we present an illustrative example. [ABSTRACT FROM AUTHOR]

In this paper, we establish sufficient conditions for the existence of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. We apply the technique of measure of noncompactness and the fixed point theorems of Darbo and Mönch. As an application, two examples are included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this article, we investigate some uniqueness and Ulam's type stability concepts for the Darboux problem of partial functional differential equations with noninstantaneous impulses and delay in Banach spaces. The main techniques rely on fractional calculus, integral equations and inequalities. Two examples are also provided to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some uniqueness and Ulam's type stability concepts for functional abstract fractional differential equations with not instantaneous impulses in Banach spaces. [ABSTRACT FROM AUTHOR]

In this article, the authors give sufficient conditions for existence and attractivity of mild solutions for second order semi-linear functional evolution equation in Banach spaces using Schauder's fixed point theorem. An example is provided to illustrate the result. [ABSTRACT FROM AUTHOR]

In this work, we propose sufficient conditions guaranteeing an existence result of mild solutions by using the nonlinear Leray-Schauder alternative in Banach spaces combined with the semigroup theory for the class of Caputo partial semilinear fractional evolution equations with finite state-dependent delay and nonlocal conditions. [ABSTRACT FROM AUTHOR]

This paper concerns for controllability of fractional order integro-differential inclusions with infinite delay in Banach spaces. A theorem about the existence of mild solutions to the controllability of fractional order integro-differential inclusions is obtained based on Dhage fixed point theorem. An example is given to illustrate the existence result. [ABSTRACT FROM AUTHOR]

In this paper we prove the existence of a mild solution for a class of impulsive semilinear evolution differential inclusions with state-dependent delay and multivalued jumps in a Banach space. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values. [ABSTRACT FROM AUTHOR]

This paper concerns the existence of mild solutions for fractional order integro-differential equations with infinite delay. Our analysis is based on the technique of Kuratowski's measure of noncompactness and Mönch's fixed point theorem. An example to illustrate the applications of main results is given. [ABSTRACT FROM AUTHOR]

In the present article we investigate the existence, uniqueness and the stability of solutions for some systems of partial integro-differential equations of fractional order in Banach and Fréchet spaces. Our techniques are based on some fixed point theorems. [ABSTRACT FROM AUTHOR]

In this article we investigate the existence of solutions on a compact interval for the fractional integro-differential inclusions with state-dependent delay in Banach spaces when the delay is infinite. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, we investigate the existence of solutions under the Pettis integrability assumption for an initial value problem for a hyperbolic differential inclusion of Caputo fractional order. We apply the measure of weak noncompactness technique. [Copyright &y& Elsevier]

In this paper we study the existence of solutions for differential equations with state dependent delay on an unbounded domain. Our results are based on the properties of the Kuratowski measure of noncompactness and Darbo's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this article, we give sufficient conditions for the existence of solutions for an integral equation of fractional order with multiple time delays in Banach spaces. Our main tool is a fixed point theorem of Mönch type associated with measures of noncompactness. Our results are illustrated by an example. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions, for a class of boundary value problem for fractional differential equations involving the Riemann-Liouville fractional derivative on an unbounded interval in Banach spaces. Our main tool is the technique of measures of noncompactness combined with Mönch's fixed point theorem and the diagonalization process. [ABSTRACT FROM AUTHOR]

In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed point theorem for the sum of completely continuous and contraction operators. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we establish sufficient conditions for existence and uniqueness of solutions for some nondensely defined semilinear functional differential equations involving the Riemann–Liouville derivative. Our approach is based on integrated semigroup theory, the Banach contraction principle, and the nonlinear alternative of Leray–Schauder type. [Copyright &y& Elsevier]

Abstract: In this paper, we shall establish sufficient conditions for the existence of integral solutions and extremal integral solutions for some nondensely defined impulsive semilinear functional differential inclusions in separable Banach spaces. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators. The question of controllability of these equations and the topological structure of the solutions set are considered too. [Copyright &y& Elsevier]