Existence and uniqueness of solutions to impulsive fractional differential equations via the deformable derivative

Abstract

In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the deformable fractional derivative. We achieve our results using classical fixed point theorems such as the Banach contraction principle, the Shaefer and the alternative Leray–Schauder theorems. We provide an example to illustrate our abstract results.