Existence and Ulam-Hyers Stability of Mild Solutions for Impulsive Integro-Differential Systems Via Resolvent Operators

Abstract

The aim of this paper is to present existence, Ulam-Hyers-Rassias stability and continuous dependence on initial conditions for the mild solution of impulsive integro-differential systems via resolvent operators. Our analysis is based on fixed point theorem with generalized measures of noncompactness, this approach is combined with the technique that uses convergence to zero matrices in generalized Banach spaces. An example is presented to illustrate the efficiency of the result obtained.