Generalized Mittag-Leffler quadrature methods for fractional differential equations

Abstract

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.