(ω,c)-Periodic Solutions to Fractional Differential Equations with Impulses

Abstract

This paper deals with the (ω,c)-periodic solutions to impulsive fractional differential equations with Caputo fractional derivative with a fixed lower limit. Firstly, a necessary and sufficient condition of the existence of (ω,c)-periodic solutions to linear problem is given. Secondly, the existence and uniqueness of (ω,c)-periodic solutions to semilinear problem are proven. Lastly, two examples are given to demonstrate our results.