Periodic boundary value problems for fractional semilinear integro-differential equations with non-instantaneous impulses

Bo Zhu,Lishan Liu

doi:10.1186/s13661-018-1048-1

Abstract

In this paper, we study periodic boundary value problems of fractional semilinear integro-differential equations with non-instantaneous impulses in Banach spaces. By the measure of noncompactness, the theory of β-resolvent family, and the fixed point theorem, we obtain several sufficient conditions on the existence of mild solutions for such problems. Finally, an example is given to show the main results of this paper.

Highlights

1 Introduction In the last decades, many researchers have been attracted to studying the fractional differential equations, and a lot of good results have been obtained, see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] and the references therein
The differential equations with non-instantaneous impulses of the following form were initially investigated by the authors in [18, 19]:
In [21, 23], the authors studied the stability of the fractional differential equations with non-instantaneous impulses

Summary

Introduction

Many researchers have been attracted to studying the fractional differential equations, and a lot of good results have been obtained, see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] and the references therein. The differential equations with non-instantaneous impulses of the following form were initially investigated by the authors in [18, 19]: In [20], authors investigated the following periodic boundary value problem of integer nonlinear evolution equations with non-instantaneous impulses:

Results

Conclusion