Existence of Solutions to Anti-Periodic Boundary Value Problem for Nonlinear Fractional Differential Equations with Impulses

Anping Chen,Yi Chen

doi:10.1155/2011/915689

Abstract

This paper discusses the existence of solutions to antiperiodic boundary value problem for nonlinear impulsive fractional differential equations. By using Banach fixed point theorem, Schaefer fixed point theorem, and nonlinear alternative of Leray-Schauder type theorem, some existence results of solutions are obtained. An example is given to illustrate the main result.

Highlights

Fractional differential equations have proved to be an excellent tool in the mathematic modeling of many systems and processes in various fields of science and engineering
The theory of impulsive differential equations has found its extensive applications in realistic mathematic modeling of a wide variety of practical situations and has emerged as an important area of investigation in recent years
Many authors are devoted to the study of boundary value problems for impulsive differential equations of integer order, see 9–12

Summary

Introduction

We consider an antiperiodic boundary value problem for nonlinear fractional differential equations with impulses. Ahmad et al in have discussed some existence results for the two-point boundary value problem involving nonlinear impulsive hybrid differential equation of fractional order by means of contraction mapping principle and Krasnoselskii’s fixed point theorem. They have obtained the existence results for integral boundary value problem of nonlinear impulsive fractional differential equations see. Tian et al in have obtained some existence results for the three-point impulsive boundary value problem involving fractional differential equations by the means of fixed points method. This paper studies the existence of solutions of antiperiodic boundary value problem for fractional differential equations with impulses.

Preliminaries

Main Result

Example