In this paper, the averaging principle for stochastic Caputo fractional differential equations with the nonlinear terms satisfying the non-Lipschitz condition is considered. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Gronwall inequality with singular integral kernel which is a key part in our analysis. Secondly, we discuss the existence and uniqueness of solution. And finally, the averaging principle is considered.

中文翻译：

---

非Lipschitz条件下随机Caputo分数阶微分方程的平均原理

本文考虑了非线性项满足非Lipschitz条件的随机Caputo分数阶微分方程的平均原理。文章中的工作大致分为三个部分。首先，我们建立了具有奇异积分核的广义Gronwall不等式，这是我们分析的关键部分。其次，讨论解的存在性和唯一性。最后，考虑平均原理。