Solvability and optimal controls of non-instantaneous impulsive stochastic neutral integro-differential equation driven by fractional Brownian motion

In this manuscript, a new class of non-instantaneous impulsive stochastic neutral integrodi fferential equation driven by fractional Brownian motion (fBm, in short) with state-dependent delay and their stochastic optimal control problem is studied. We utilize the theory of the resolvent operator and a fixed point technique to present the solvability of the stochastic system. Then, the existence of optimal controls is discussed for the proposed stochastic system. Finally, an example is offered to demonstrate the obtained theoretical results.