The existence of solutions for boundary value problems of two types fractional perturbation differential equations

Abstract

In this paper, we study the existence of solutions for the boundary value problems of fractional perturbation differential equationssubject towhere 1 < α < 2, D α is the standard Caputo fractional derivatives. Using some fixed point theorems, we prove the existence of solutions to the two types. For each type we give an example to illustrate our results.