Approximate solution of fractional integro-differential equations by Taylor expansion method

被引：91

作者：

Huang, Li ^{[1
]}

Li, Xian-Fang ^{[2
]}

Zhao, Yulin ^{[1
]}

Duan, Xiang-Yang ^{[1
]}

机构：

[1] Hunan Univ Technol, Coll Sci, Zhuzhou 412008, Hunan, Peoples R China

[2] Cent South Univ, Changsha 410083, Hunan, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 62卷 / 03期

关键词：

Fractional integro-differential equation; Taylor expansion; Approximate solution; Riemann-Liouville; Fredholm equations; Volterra equations; NUMERICAL-SOLUTION;

D O I：

10.1016/j.camwa.2011.03.037

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, Taylor expansion approach is presented for solving (approximately) a class of linear fractional integro-differential equations including those of Fredholm and of Volterra types. By means of the mth-order Taylor expansion of the unknown function at an arbitrary point, the linear fractional integro-differential equation can be converted approximately to a system of equations for the unknown function itself and its m derivatives under initial conditions. This method gives a simple and closed form solution for a linear fractional integro-differential equation. In addition, illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1127 / 1134

页数：8

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