A fixed-point theoretic approach for controllability result of retarded nonlocal condition-based semilinear systems

In this research, our focus lies on investigating a set of new sufficient conditions to establish the controllability result for a class of semilinear systems described by retarded integrodifferential equations with nonlocal conditions. To achieve this, we employ Sadovskii’s fixed-point theorem in conjunction with the principles of \(C_0\) $C_0$ -semigroup theory and the compact nature of the nonlinear function. Additionally, we offer an illustrative example to showcase and clarify the analytical findings presented in the study.