  This paper uses the resolvent operator technique to investigate second-order
non-autonomous neutral integrodifferential equations with impulsive conditions
in a Banach space. We study the existence of a mild solution and the system's
approximate controllability. The semigroup and resolvent operator theory, graph
norm, and Krasnoselskii's fixed point theorem are used to demonstrate the
results. Finally, we present our findings with an example.
