Recent studies on boundary value problems for impulsive fractional differential systems involving Caputo fractional derivatives

Abstract

We present a new method to convert the boundary value problems for impulsive fractional differential equations involving Caputo fractional derivatives to integral equations. This method is used to solve a classes of boundary value problems for impulsive fractional differential equations. Moreover, some new results on the existence of solutions of anti-periodic boundary value problems for impulsive fractional differential systems are established (see Sect. 3). Our analysis relies on the well known Schauder’s fixed point theorem. Some examples and comments on recent published papers are given to illustrate the differences between our main theorems and known results.