Results on approximate controllability of neutral integro-differential stochastic system with state-dependent delay

This article is mainly focusing on the approximate controllability of neutral integro-differential stochastic equations with state-dependent delay. The main results of this article are proved by applying some ideas about the semigroup theory and resolvent operators. At first, the investigation about the existence of a mild solution and then we discuss the approximate controllability of the considered system. Next, we extend our study to the system with non-local conditions. Finally, a theoretical application is presented for proving the validity of controllability results obtained.