On the approximate controllability of second-order stochastic differential systems with hemivariational inequalities with damping

In this article, we investigate the approximate controllability of damping second-order stochastic differential systems with hemivariational inequalities. First, we show the existence of a mild solution to the suggested second-order differential system with the notions of generalized Clarke's subdifferential type. Next, by adopting the fixed point technique of condensing multi-valued maps, the conditions for generalized Clarke's subdifferential and the strongly continuous cosine family is employed for the existence of a mild solution. Furthermore, the approximate controllability results for the given system are proven. In the end, an illustration is presented to highlight our primary findings.