Existence results for an impulsive neutral integro-differential equations in Banach spaces

In this manuscript we investigate the existence of mild solution for a abstract impulsive neutral integro-differential equation by using semi-group theory and Krasnoselskii-Schaefer fixed point theorem in different approach. At last, an example is also provided to illustrate the obtained results.

Existence theory of fractional coupled differential equations via Ψ-Hilfer fractional derivative

In this paper, we analyze existence results for coupled differential equations via ψ- Hilfer fractional derivative. The proof relies on the Schaefer fixed point theorem.

Control of bounded solutions for first-order singular differential equations with impulses

This paper is concerned with a kind of first-order singular differential system with impulses. Based on the Schaefer fixed-point theorem, some new verifiable algebraic criteria are given to ensure the controllability of bounded solutions for the considered system. The results obtained in this paper not only achieve the controllability of the singular differential system with impulses for the first time, but also complement the previous researches on singular differential system with impulses. Consequently, the results established are essentially new. Finally, the effectiveness of the obtained results are illustrated via a numerical example.

Energy-dependent fractional Sturm-Liouville impulsive problem

In study, we show the existence and integral representation of solution for energy-dependent fractional Sturm-Liouville impulsive problem of order with ? ? (1,2] impulsive and boundary conditions. An existence theorem is proved for energy-dependent fractional Sturm-Liouville impulsive problem by using Schaefer fixed point theorem. Furthermore, in the last part of the article, an application is given for the problem and visual results are shown by figures.

A coupled system of nonlinear differential equations involving m nonlinear terms

In this paper, we study a coupled system of nonlinear fractional differential equations involving m nonlinear terms, ${m\in\mathbb{N^{*}}}$. We begin by introducing a new Banach space. Then, we establish new existence and uniqueness results using the Banach contraction principle. We also prove an existence result using the Schaefer fixed point theorem. Finally, we give some illustrative examples.

Existence Uniqueness Theorems for Multi-Term Fractional Delay Differential Equations

In this paper we analyze non-linear multi-term fractional delay differential Equationdenotes the Caputo fractional derivative of order α. The Schaefer fixed point theorem and Banach contraction principle are used to investigate the existence and uniqueness of solutions for above equation with periodic/ anti-periodic boundary conditions.

Fractional Differential Equations with Fractional Impulsive and Nonseparated Boundary Conditions

This paper studies the existence results for nonseparated boundary value problems of fractional differential equations with fractional impulsive conditions. By means of Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. Examples are given to illustrate the results.

Existence of Solutions of a Class of Abstract Second Order Nonlinear Integrodifferential Equations

In this paper we prove the existence of solutions of nonlinear second order integrodifferential equations in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of operators and the Schaefer fixed point theorem.

A note on controllability of semilinear integrodifferential systems in Banach spaces

Sufficient conditions for controllability of semilinear integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem.

Controllability of nonlinear Volterra integrodifferential systems with prescribed controls

Sufficient conditions for the global controllability of nonlinear Volterra integrodifferential systems with prescribed controls are derived. The method is a transformation of the given control system into a boundary value problem and then the result is obtained by the application of the Schaefer fixed point theorem.