Approximate controllability of non-autonomous evolution system with infinite delay

This article deals with the existence and approximate controllability results for a class of nonautonomous second-order evolution systems with infinite delay. To establish sufficient conditions for the proposed control problem the theory of evolution operator with Schauder’s fixed point theorem is used. Further, we extend the approximate controllability results to the integro-impulsive differential system. Finally, to emphasize our theoretical concepts, an example is provided.