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

by *,† and
School of Sciences, Shanghai Institute of Technology, Shanghai 201418, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2018, 10(10), 503; https://doi.org/10.3390/sym10100503
Received: 15 September 2018 / Revised: 3 October 2018 / Accepted: 11 October 2018 / Published: 15 October 2018
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. View Full-Text
Keywords: Mittag–Leffler function; fractional calculus; fractional derivative; fractional differential equation Mittag–Leffler function; fractional calculus; fractional derivative; fractional differential equation
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MDPI and ACS Style

Duan, J.; Chen, L. Solution of Fractional Differential Equation Systems and Computation of Matrix Mittag–Leffler Functions. Symmetry 2018, 10, 503. https://doi.org/10.3390/sym10100503

AMA Style

Duan J, Chen L. Solution of Fractional Differential Equation Systems and Computation of Matrix Mittag–Leffler Functions. Symmetry. 2018; 10(10):503. https://doi.org/10.3390/sym10100503

Chicago/Turabian Style

Duan, Junsheng, and Lian Chen. 2018. "Solution of Fractional Differential Equation Systems and Computation of Matrix Mittag–Leffler Functions" Symmetry 10, no. 10: 503. https://doi.org/10.3390/sym10100503

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