The theory of averaging is a classical component of applied mathematics and has been applied to solve some engineering problems, such as in the filed of control engineering. In this paper, we develop a theory of averaging on both finite and infinite time intervals for fractional non-autonomous differential equations. The closeness of the solutions of fractional no-autonomous differential equations and the averaged equations has been proved. The main results of the paper are applied to the switched capacitor voltage inverter modeling problem which is described by the fractional differential equations.

中文翻译：

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分数阶微分方程的平均理论

平均理论是应用数学的经典组成部分，已被用于解决一些工程问题，例如控制工程领域。在本文中，我们建立了分数非自治微分方程的有限和无限时间间隔平均的理论。证明了分数阶非自治微分方程和平均方程解的接近性。本文的主要结果被应用于由分数阶微分方程描述的开关电容器电压逆变器建模问题。