Solution of Fractional Differential Equation Systems and Computation of Matrix Mittag–Leffler Functions

Abstract

In this paper, solutions for systems of linear fractional differential equations are considered. For the commensurate order case, solutions in terms of matrix Mittag–Leffler functions were derived by the Picard iterative process. For the incommensurate order case, the system was converted to a commensurate order case by newly introducing unknown functions. Computation of matrix Mittag–Leffler functions was considered using the methods of the Jordan canonical matrix and minimal polynomial or eigenpolynomial, respectively. Finally, numerical examples were solved using the proposed methods.

Keywords

• Mittag–Leffler function
• fractional calculus
• fractional derivative
• fractional differential equation