A generalization of the Mittag-Leffler function and solution of system of fractional differential equations

被引：10
|
作者：
Duan, Junsheng [1 ]
机构：
[1] Shanghai Inst Technol, Sch Sci, Shanghai, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2018年
基金：
中国国家自然科学基金;
关键词：
Fractional calculus; Fractional derivative; Mittag-Leffler function; Fractional differential equation; SYNCHRONIZATION; DERIVATIVES; RELAXATION; DIFFUSION;
D O I：
10.1186/s13662-018-1693-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The solutions of system of linear fractional differential equations of incommensurate orders are considered and analytic expressions for the solutions are given by using the Laplace transform and multi-variable Mittag-Leffler functions of matrix arguments. We verify the result with numeric solutions of an example. The results show that the Mittag-Leffler functions are important tools for analysis of a fractional system. The analytic solutions obtained are easy to program and are approximated by symbolic computation software such as MATHEMATICA.
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页数：12
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