This article investigates the existence of a solution for a class of fractional delayed stochastic differential equations with noninstantaneous impulses and fractional Brownian motion (fBm). Utilizing the theory of fractional calculus, stochastic integrals for fBm and fixed-point technique, we obtain the solvability result for the considered system. Next, we formulate a fractional stochastic optimal control problem for the infinite delayed impulsive system. Finally, the existence of an optimal state-control pair is established using the Balder Theorem. An example is also constructed that exhibits the efficiency of our results.

This manuscript explores a new class of non-autonomous second-order stochastic inclusions of Clarke?s subdifferential form with non-instantaneous impulses (NIIs), unbounded delay, and the Rosenblatt process in Hilbert spaces. The existence of a solution is deduced by employing a fixed point strategy for a set-valued map together with the evolution operator and stochastic analysis approach. An example is analyzed for theoretical developments.

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