An Efficient Method for Solving Systems of Linear Ordinary and Fractional Differential Equations
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- 作者：Mohsen Didgar ; Nafiseh Ahmadi
- 关键词：System of ordinary differential equations ; System of fractional differential equations ; Riemann–Liouville fractional derivative ; Taylor expansion ; 34A08 ; 65L05
- 刊名：Bulletin of the Malaysian Mathematical Sciences Society
- 出版年：2015
- 出版时间：October 2015
- 年：2015
- 卷：38
- 期：4
- 页码：1723-1740
- 全文大小：782 KB
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Nafiseh Ahmadi (2)
1. Department of Mathematics, Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran
2. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran - 刊物类别：Mathematics, general; Applications of Mathematics;
- 刊物主题：Mathematics, general; Applications of Mathematics;
- 出版者：Springer Singapore
- ISSN：2180-4206
文摘
This paper presents a reliable approach for solving linear systems of ordinary and fractional differential equations. First, the FDEs or ODEs of a system with initial conditions to be solved are transformed to Volterra integral equations. Then Taylor expansion for the unknown function and integration method are employed to reduce the resulting integral equations to a new system of linear equations for the unknown and its derivatives. The fractional derivatives are considered in the Riemann–Liouville sense. Some numerical illustrations are given to demonstrate the effectiveness of the proposed method in this paper. Keywords System of ordinary differential equations System of fractional differential equations Riemann–Liouville fractional derivative Taylor expansion