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This paper uses the resolvent operator technique to investigate second-ordernon-autonomous neutral integrodifferential equations with impulsive conditionsin a Banach space. We study the existence of a mild solution and the system'sapproximate controllability. The semigroup and resolvent operator theory, graphnorm, and Krasnoselskii's fixed point theorem are used to demonstrate theresults. Finally, we present our findings with an example.

Controllability of a second-order impulsive neutral differential equation via resolvent operator technique