The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators

In this manuscript, we investigate the solvability and optimal controls for impulsive fractional stochastic integro-differential equations in Hilbert space. Sufficient conditions are obtained for the existence of mild solution of the considered system by using analytic resolvent operators, the uniform continuity of the resolvent, and Leray–Schauder fixed point theorem. Then, the existence of optimal controls is discussed for the considered system. Finally, the obtained theoretical result is validated through an example.