Algorithm for solving the Cauchy problem for stationary systems of fractional order linear ordinary differential equations

被引：6

作者：

Aliev, Fikrat Ahmadali ^{[1
]}

Aliev, Nihan ^{[1
]}

Safarova, Nargis ^{[1
]}

Velieva, Naila ^{[1
]}

机构：

[1] BSU, Inst Appl Math, Baku, Azerbaijan

来源：

COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS | 2020年 / 8卷 / 01期

关键词：

Cauchy problem; linear fractional derivative system; Mittag-Leffler function; constant matrix coefficients; EXISTENCE;

D O I：

10.22034/cmde.2019.9526

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new simplified analytical formula is given for solving the Cauchy problem for a homogeneous system of fractional order linear differential equations with constant coefficients (SFOLDECC). The exponential function matrix in this formula is replaced by a Taylor series. Next, an analytical expression of the integral is obtained, with the help of which, for the transition matrix, a relation is obtained that allows one to obtain a solution of the Cauchy problem with high accuracy. The results also apply to the case of inhomogeneous systems with constant perturbations and are illustrated by numerical examples.

引用

页码：212 / 221

页数：10

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