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.

No abstract

No abstract

No abstract

The problem of approximate controllability is investigated in this paper for a class of fractional stochastic differential equations driven by fractional Brownian motion with non‐instantaneous impulses and Poisson jumps. The results are obtained by employing the η‐resolvent family and Krasnoselskii's fixed point theorem. Further, we derive the trajectory controllability for the proposed stochastic control system. Finally, an example is provided to illustrate the obtained theory.