Nonlocal Second Order Delay Semilinear Integro-Differential Time Varying Evolution Equation with Convex-Power Condensing Operators

Abstract

In this paper, we present findings concerning the existence of solutions to a particular type of nonlocal second-order delay semilinear integro-differential equation with time-varying evolution. We utilize the theory of the resolvent family, the Kuratowski measure of noncompactness, and fixed point theorems in conjunction with a convex-power condensing operator to establish novel and sufficient conditions for ensuring the existence of mild solutions. Finally, we provide an illustrative example to demonstrate the validity of the proposed results.