Resolvent Operator Method for Controllability in Non-autonomous Second Order Stochastic Integrodifferential Systems with Clarke Subdifferential

This work aims to investigate a new class of non-autonomous second order stochastic integrodifferential systems involving Clarke subdifferential. The properties of the resolvent operator associated with the non-autonomous second order differential system, together with a multivalued fixed point approach and stochastic analysis, are employed to verify the existence of mild solution for the proposed system. Furthermore, we analyze the approximate controllability of the system under the assumption that the corresponding linear system is approximately controllable. Finally, an illustrative example is presented to support the theoretical results.