Stability of stochastic differential equations driven by Lévy noise with Markovian switching has recently received a lot of attention. Different from the integer-order stochastic differential equations, stochastic fractional differential equations play a circular role in describing many practical processes and systems. In this paper, our aims are to study the averaging principle of the solution of hybrid stochastic fractional differential equations driven by Lévy noise under non-Lipschitz conditions which include classical Lipschitz conditions as special cases and propose several sufficient conditions for asymptotic stability in the pth moment of the solution. Two examples with numerical simulation are given to illustrate the obtained theory.

中文翻译：

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Lévy噪声驱动的混合随机分数阶微分方程的平均原理及稳定性

由 Lévy 噪声驱动的带有马尔可夫转换的随机微分方程的稳定性最近受到了很多关注。与整数阶随机微分方程不同，随机分数阶微分方程在描述许多实际过程和系统时起着循环作用。在本文中，我们的目的是研究在非 Lipschitz 条件下由 Lévy 噪声驱动的混合随机分数阶微分方程解的平均原理，其中包括经典的 Lipschitz 条件作为特例，并提出了 pth 时刻渐近稳定的几个充分条件的解决方案。给出了两个数值模拟的例子来说明所得到的理论。