Abstract This paper presents an averaging principle for fractional stochastic differential equations in ℝn with fractional order 0 < α < 1. We obtain a time-averaged equation under suitable conditions, such that the solutions to original fractional equation can be approximated by solutions to simpler averaged equation. By mathematical manipulations, we show that the mild solution of two equations before and after averaging are equivalent in the sense of mean square, which means the classical Khasminskii approach for the integer order systems can be extended to fractional systems.

中文翻译：

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分数阶 0 < α < 1 随机微分方程的平均原理

摘要 本文提出了分数阶为 0 < α < 1 的 ℝn 分数阶随机微分方程的平均原理。我们得到了一个合适条件下的时间平均方程，使得原始分数方程的解可以近似为更简单平均的解。方程。通过数学运算，我们表明平均前后两个方程的温和解在均方意义上是等价的，这意味着整数阶系统的经典Khasminskii方法可以扩展到分数系统。