This paper, focusing on the fractional neutral stochastic differential equations (FNSDEs) in the Euclidean space ${\mathbb{R}}^n$, successfully provides the first evidence of a new fractional averaging theorem via rigorous mathematical deductions. With the help of integration by part, the fractional term is handled simply and ingeniously. Based on this new idea, we show that the mild solutions of two fractional systems before and after averaging are equivalent in mean square sense. The study here gives a general approach to come up with the Khasminskii averaging principle for FNSDEs.

中文翻译：

---

分数阶中立型随机方程的有效平均理论 $0<\alpha <\mathrm{1个}$ 泊松跳

本文着重于欧氏空间中的分数中立随机微分方程（FNSDEs） ${\mathbb{[R}}^{ñ}$通过严格的数学推论，成功地提供了新的分数平均定理的第一个证据。借助部分积分，简单而巧妙地处理了分数项。基于此新思想，我们表明在均方意义上，求平均值前后的两个分数系统的温和解是等效的。这里的研究给出了提出FNSDE的Khasminskii平均原理的一般方法。