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 techniques, 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 for the system under certain assumptions. Some examples are given to illustrate the abstract results.