Existence of solution for impulsive fractional differential equations with nonlocal conditions by topological degree theory

Abstract

This article aims to investigate the existence and uniqueness of solutions to impulsive fractional differential equations. Firstly, we show a formula for solutions to an impulsive fractional problem involving a generalization of the classical Caputo derivative with a nonlocal condition in a Banach space. Secondly, some sufficient conditions for the existence of solutions are established by applying fixed point methods. Furthermore, we reconsider some of operators for deriving the existence and uniqueness of the solution to impulsive fractional problem using topological degree techniques. The results support this in one example.