Optimal controls for second-order stochastic differential equations driven by mixed-fractional Brownian motion with impulses

We study optimal control problems for a class of second-order stochastic differential equation driven by mixed-fractional Brownian motion with non-instantaneous impulses. By using stochastic analysis theory, strongly continuous cosine family, and a fixed point approach, we establish the existence of mild solutions for the stochastic system. Moreover, the optimal control results are derived without uniqueness of mild solutions of the stochastic system. Finally, the main results are validated with the aid of an example.