In this paper, we propose a generalized Mittag-Leffler quadrature method for solving linear fractional differential equations with a forcing term. The construction of such a scheme is based on the variation-of-constants formula which has a generalized Mittag-Leffler function in the kernel, and incorporates the idea of collocation methods and the local Fourier expansion of the system. The properties of the methods are analyzed. The numerical experiments show the high effectiveness of the new methods.

中文翻译：

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分数阶微分方程的广义Mittag-Leffler正交方法

在本文中，我们提出了一种广义的Mittag-Leffler正交方法，用于求解带有强迫项的线性分数阶微分方程。这种方案的构造是基于常数变化公式，该公式在内核中具有广义的Mittag-Leffler函数，并结合了配置方法的思想和系统的局部Fourier展开。分析了方法的性质。数值实验表明了新方法的有效性。