In this article, we study the stochastic fractional optimal control problem for a system governed by a class of non-instantaneous impulsive stochastic fractional differential equation in the infinite-dimensional spaces. We utilize the fractional calculus, stochastic analysis theory and a suitable fixed point approach to present the solvability of the stochastic fractional system. Then, the existence of optimal state-control pairs of the Lagrange problem is derived without uniqueness of solutions of the stochastic system. Finally, the main results are validated with the aid of an example.

中文翻译：

---

q∈（1,2）阶非瞬时脉冲随机分数阶微分方程的可解性和最优控制

在本文中，我们研究了在无限维空间中由一类非瞬时脉冲随机分数阶微分方程控制的系统的随机分数最优控制问题。我们利用分数演算，随机分析理论和合适的不动点方法来介绍随机分数系统的可解性。然后，在没有随机系统解唯一性的情况下，得出了拉格朗日问题的最优状态控制对的存在。最后，通过一个例子验证了主要结果。