Mild solution for an impulsive non-autonomous neutral differential equation with a deviated argument

Abstract

In the present work, we investigate the existence of the mild solution for an impulsive non-autonomous neutral differential equation with a deviated argument in an arbitrary complex Banach space E. We firstly establish the existence and uniqueness of the mild solution to impulsive neutral differential equation with deviated argument by using Banach fixed point theorem. The second existence result is obtained by using Kranoselskii fixed point theorem. An example is also provided to show the applicability of obtained theory.