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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.

This paper discusses the global convergence of successive approximations methods for solving integro-differential equation via resolvent operators in Banach spaces. We prove a theorem on the global convergence of successive approximations to the unique solution of the problems. An example is given to show the application of our result.

The aim of this paper is to study the existence of the unique mild solution for non-linear fractional integro-differential equations with state-dependent nonlocal condition. The result was obtained by using nonlinear alternative of Granas-Frigon for contraction in Fréchet spaces. To illustrate the result, an example is provided.

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.

In this paper, we shall establish sufficient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdorff measure, noncompactness and Tikhonoff’s fixed point theorem. We give an example for illustration.

In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.

This research investigates the existence of piecewise asymptotically almost automorphic mild solutions for integrodifferential equations with infinite delay. The existence results are proved by using the Mönch's fixed point theorem, the concept of measures of non-compactness theorem and resolvent operator. Finally, an example is presented to illustrate our obtained results. [ABSTRACT FROM AUTHOR]

The purpose of this study is to use resolvent operators to investigate the existence and the controllability of a mild solution to a second-order semilinear integro-differential problem. To construct our criterion, we use a fixed point theorem in conjunction with measures of noncompactness. A practical example is used to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

The primary focus of this study is to explore the presence of a mild solution within a specific category of fractional non-autonomous differential evolution equations, incorporating integral impulse conditions. The approach employed extends the classical Darbo fixed point theorem for Fréchet spaces, leveraging the notion of a measure of noncompactness along with the principle of K-set contraction. To illustrate our findings, we offer an illustrative example. [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 this manuscript, we investigate the issue of approximate controllability for a certain class of abstract neutral integro-differential equations having non-instantaneous impulsions and being subject to state-dependent delay. Our methodology relies on the utilization of resolvent operators in conjunction with Darbo's fixed point theorem. To exemplify the practical implications of our findings, we provide an illustration. [ABSTRACT FROM AUTHOR]

This paper addresses some existence, attractivity and controllability results for semilinear integrodifferential equations having non-instantaneous impulsions on an infinite interval via resolvent operators in case of neutral and state-dependent delay problems. Our criteria were obtained by applying a Darbo's fixed-point theorem combined with measures of noncompactness. The obtained result is illustrated by an example at the end. [ABSTRACT FROM AUTHOR]

In this article, we study some existence and controllability results for two classes of second order functional differential equations with delay and random effects. To begin, we employ a random fixed point theorem with a stochastic domain to demonstrate the existence of mild random solutions. Next, we prove that our problems are controllable. Finally, an example is given to validate the theory part. [ABSTRACT FROM AUTHOR]

This paper deals with some existence of bounded solutions for two classes of semlinear differential equations. We consider the cases when the linear part of the equation generates a C0 semigroup as well as an integrated semigroup. An application is made of a Darbo fixed point theorem associated with the diagonalization method and the concept of measure of noncompactness. The present results initiate the application of such method to semilinar differential equations on the half line. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the existence of asymptotically almost automorphic mild solution to some classes of second order semilinear evolution equation via the techniques of measure of noncompactness. The investigation is based on a new fixed point result which is a generalization of the well known Darbo's fixed point theorem. Finally examples are given to illustrate the analytical findings. [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 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]

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 the existence of mild and integral solutions for a class of functional differential equations. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of 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]

This paper deals with the existence of mild solutions for impulsive fractional order stochastic integro-differential inclusions with state-dependent delay. The existence result is obtained by using a fixed point technique on a Hilbert space. An illustrating example is presented. [ABSTRACT FROM AUTHOR]

Our aim in this work is to study the existence of solutions of first and second order functional differential equations with state-dependent delay. We use the Mönch’s fixed point theorem for the existence of solutions and the concept of measures of noncompactness. [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]

The authors study the existence of mild solutions to a functional differential equation with delay and random effects. They use a random fixed point theorem with a stochastic domain. An example is included to illustrate their results. [ABSTRACT FROM AUTHOR]

In this paper, we provide sufficient conditions for the existence of mild solutions for a class of impulsive fractional evolution equations with state-dependent delay. The results are obtained by using the nonlinear alternative of Leray-Schauder type fixed point theorem. An example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay. We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions. [ABSTRACT FROM AUTHOR]

In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory. [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 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]

In this paper sufficient conditions are given ensuring the controllability of mild solutions defined on a bounded interval for two classes of first order semilinear functional and neutral functional differential equations involving evolution operators when the delay is infinite using the nonlinear alternative of Leray-Schauder type. [ABSTRACT FROM AUTHOR]

In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for two classes of first order semilinear functional and neutral functional differential evolution inclusions with infinite delay using a recent nonlinear alternative for contractive multivalued maps in Fréchet spaces due to Frigon, combined with semigroup theory. [ABSTRACT FROM AUTHOR]

This article shows sufficient conditions for the existence of mild solutions, on the positive half-line, for two classes of first-order functional and neutral functional perturbed differential evolution equations with infinite delay. Our main tools are: the nonlinear alternative proved by Avramescu for the sum of contractions and completely continuous maps in Fréchet spaces, and the semigroup theory. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a recent nonlinear alternative for multivalued admissible contractions in Fréchet spaces due to Frigon combined with semigroups theory is used to investigate the controllability of some classes of semilinear functional and neutral functional differential inclusions in Fréchet spaces. [Copyright &y& Elsevier]

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]