Abstract The aim of this paper is to investigate a class of nonlinear stochastic reaction-diffusion systems involving fractional Laplacian in a bounded domain. First, the existence and uniqueness of weak solutions are proved by using Galërkin’s method. Second, the existence of optimal controls for the corresponding stochastic optimal control problem is obtained. Finally, several examples are provided to demonstrate the theoretical results.

中文翻译：

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随机分数反应扩散系统的弱解与最优控制

摘要 本文的目的是研究一类在有界域中涉及分数拉普拉斯算子的非线性随机反应扩散系统。首先，利用Galërkin方法证明了弱解的存在唯一性。其次，获得了对应随机最优控制问题的最优控制的存在性。最后，提供了几个例子来证明理论结果。