A Note on the Existence and Optimal Control of Atangana–Baleanu Fractional Stochastic Integrodifferential System With Noninstantaneous Impulses

This study is concerned with the existence of mild solution and optimal control for the Atangana–Baleanu fractional stochastic integrodifferential system with noninstantaneous impulses in Hilbert spaces. We verify the existence of mild solution for the considered system through fractional calculus, stochastic analysis, semigroup theory, and the Leray–Schauder fixed point theorem. Likewise, with the construction of a Bolza problem, we determine the existence of optimal control for the fractional stochastic system. Furthermore, an example is offered to verify our theoretical results.