Abstract
In this paper, we derive the controllability results for nonlocal and impulsive integro-differential equations, with finite delay, in a Hilbert space using the resolvent operator theory. For this, we first convert the controllability problem into a fixed point problem to show the existence of a mild solution of the system and then establish the approximate controllability of the system. The main tools applied in our analysis are semigroup theory, the resolvent operator theory, and fixed point theorems. Finally, we provide two examples to show the application of our main results.
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