In this paper, we present a mathematical model of fractional order semi-linear functional stochastic differential equations with impulsive effects in a Hilbert space. The sufficient conditions of the existence and uniqueness of mild solutions for the considered problem are proved by using the classical fixed point theorems. Finally, we presented two examples to verify the results.

中文翻译：

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具状态依赖时滞的分数阶半线性随机脉冲微分方程的可解性

在本文中，我们提出了在希尔伯特空间中具有脉冲效应的分数阶半线性泛函随机微分方程的数学模型。通过使用经典不动点定理，证明了所考虑问题的温和解的存在性和唯一性的充分条件。最后，我们提供了两个示例来验证结果。