Title: Matrix Mittag-Leffler function and solution of multi-term fractional differential equations

Authors: Junsheng Duan; Lian Chen

Addresses: School of Sciences, Shanghai Institute of Technology, Shanghai 201418, China ' School of Sciences, Shanghai Institute of Technology, Shanghai 201418, China

Abstract: In this paper, we first derive the solution of fractional differential equation system expressed in matrix Mittag-Leffler function by using the Adomian decomposition method. Then we consider the initial value problem (IVP) for multi-term fractional differential equation. By introducing new unknown functions, we rewrite the IVP for multi-term fractional differential equation into the IVP for a fractional differential equation system. Thus the solution can be given in terms of matrix Mittag-Leffler functions. We demonstrate the method using four numerical examples and the results are simulated using MATHEMATICA 8.

Keywords: fractional calculus; fractional derivative; Mittag-Leffler function; fractional differential equation.

DOI: 10.1504/IJDSDE.2020.111478

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.5, pp.401 - 414

Received: 30 Apr 2018
Accepted: 02 Feb 2019

Published online: 15 Nov 2020 *

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