Optimal controllability for multi-term time-fractional stochastic systems with non-instantaneous impulses

In the present paper, we study the existence and optimal controllability of a multi-term time-fractional stochastic system with non-instantaneous impulses. Using semigroup theory, stochastic analysis theory, and Krasnoselskii’s fixed point theorem, we first establish the existence of a mild solution. Further, we obtain that there exists an optimal state-control pair of the system. Some examples are given to illustrate the abstract results.