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.

中文翻译：

---

非瞬时脉冲分数随机延迟系统的最优控制问题

本文研究了一类具有非瞬时脉冲和分数布朗运动 (fBm) 的分数阶延迟随机微分方程的解的存在性。利用分数阶微积分理论、fBm 的随机积分和不动点技术，我们获得了所考虑系统的可解性结果。接下来，我们制定了无限延迟脉冲系统的分数随机最优控制问题。最后，使用 Balder 定理建立最优状态控制对的存在。还构建了一个示例来展示我们结果的效率。