Existence outcomes and optimal control of non-autonomous second order integrodifferential system with impulsive effects via resolvent operator in Banach spaces

We consider the optimal control of a non-autonomous second order integrodifferential equation involving impulses in Banach spaces, formulated via the resolvent operator. This study centers on establishing the existence of mild solution for the control system by applying the properties of the resolvent operator associated with the non-autonomous second order integrodifferential system, along with a fixed point technique. Subsequently, we establish the existence of optimal control. To illustrate the results, we present a non-autonomous partial integrodifferential control system of second order with impulses.