This paper is concerned with Hilfer fractional stochastic delay differential equations with Poisson jumps. Under some assumptions, we obtain an averaging principle for the solution of the considered system. The required results are obtained based on fractional calculus, Doob’s martingale inequality and Cauchy–Schwarz inequality.

中文翻译：

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具有泊松跳跃的希尔弗分数阶随机时滞微分方程的平均原理

本文涉及具有泊松跳跃的希尔弗分数阶随机时滞微分方程。在某些假设下，我们获得了所考虑系统求解的平均原理。根据分数演算，Doob的s不等式和Cauchy-Schwarz不等式获得所需的结果。