In this paper, we introduce the mild solution for a new class of noninstantaneous and nonlocal impulsive Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps. The existence of the mild solution is derived for the considered system by using fractional calculus, stochastic analysis and Sadovskii’s fixed point theorem. Finally, an example is also given to show the applicability of our obtained theory.

中文翻译：

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具有分数布朗运动和泊松跳跃的非瞬时脉冲和非局部Hilfer分数阶随机积分微分方程

在本文中，我们介绍了一类新型的非瞬时和非局部脉冲希尔伯分数分数阶随机积分微分方程的温和解，该方程具有分数布朗运动和泊松跳跃。通过分数阶微积分，随机分析和Sadovskii不动点定理，得出了所考虑系统的温和解的存在性。最后，通过一个例子说明了所获得理论的适用性。