This article addresses new applications of the generalized Mittag-Leffler input stability to the fractional-order electrical circuits. We consider the fractional-order electrical circuits in the context of the generalized Caputo-Liouville derivative. We propose the Lyapunov characterizations of the fractional differential equations. A new numerical discretization, including the fractional differential equations represented by the generalized Caputo derivative, has been successfully applied to the fractional electrical circuits. To support the results, we have proposed the graphics generated by our numerical discretization. The graphics of the solutions have been analyzed and interpreted in the context of generalized Mittag-Leffler input stability and the generalized Mittag-Leffler stability. The generalized Mittag-Leffler input stability is a new stability notion for the fractional differential equations recently introduced in the literature.

中文翻译：

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分数阶电路的广义Mittag-Leffler输入稳定性

本文介绍了广义Mittag-Leffler输入稳定性在分数阶电路中的新应用。我们在广义Caputo-Liouville导数的背景下考虑分数阶电路。我们提出分数阶微分方程的Lyapunov刻画。一种新的数字离散化，包括由广义Caputo导数表示的分数阶微分方程，已成功地应用于分数电路。为了支持结果，我们提出了通过数字离散化生成的图形。解决方案的图形已经在广义Mittag-Leffler输入稳定性和广义Mittag-Leffler稳定性的背景下进行了分析和解释。