A note on existence results for noninstantaneous impulsive integrodifferential systems

Abstract

A class of noninstantaneous impulsive integrodifferential systems in Banach space will be the focus of the research presented in this paper. First, we formulate the existence and uniqueness of mild solutions for the considered equation with local initial conditions. The problem is then solved step by step using the resolvent operator in the sense of Grimmer combined with the Banach contraction theorem. In addition, considering the scenario in which we provide our system with nonlocal initial conditions, Krasnoselskii's fixed point theorem is utilized to establish mild solutions. To illustrate the theory, we will look at two different examples.