Stochastic differential equations represent equipment in modeling of a dynamic systems operating with fuzzy settings driven by stochastic noise. In this manuscript, a new kind of equation, namely fuzzy fractional stochastic differential system (FSDS) is proposed. It is defined by stochastic integral of a fuzzy process with respect to the m-dimensional Brownian motion. In this paper, the existence and uniqueness results are obtained for impulsive fuzzy FSDS with granular derivative using contraction principle. Finally, we provide a numerical example for the effectiveness of the theoretical results.

中文翻译：

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脉冲模糊分数阶随机微分系统的存在性

随机微分方程表示动态系统建模中的设备，该系统以随机噪声驱动的模糊设置运行。在该手稿中，提出了一种新的方程，即模糊分数随机微分系统（FSDS）。它是由关于m维布朗运动的模糊过程的随机积分定义的。本文利用收缩原理，得到了具有颗粒导数的脉冲模糊FSDS的存在性和唯一性。最后，我们提供了一个数值示例来说明理论结果的有效性。