An Analysis on the Optimal Control for Fractional Stochastic Delay Integrodifferential Systems of Order 1 < γ < 2

The purpose of this paper is to investigate the optimal control for fractional stochastic integrodifferential systems of order 1 < gamma < 2. To ensure the existence and uniqueness of mild solutions, we first gather a novel list of requirements. Further, the existence of optimal control for the stated issue is given by applying Balder's theorem. Additionally, we extend our existence outcomes with infinite delay. The outcomes are obtained via fractional calculus, Holder's inequality, the cosine family, stochastic analysis techniques, and the fixed point approach. The theory is shown by an illustration, as well.