A new operational matrix for solving fractional-order differential equations
A new operational matrix for solving fractional-order differential equations
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DOI：
10.1016/j.camwa.2009.07.006
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发表时间：
2010-02-01
影响因子：
2.9
通讯作者：
Dehghan, Mehdi
中科院分区：
文献类型：
--
作者：
Saadatmandi, Abbas;Dehghan, Mehdi
分数阶微积分已被用于对物理和工程过程进行建模，这些过程被发现用分数阶微分方程描述最为合适。因此，我们需要一种可靠且高效的分数阶微分方程求解技术。本文研究一类分数阶微分方程的数值解。分数阶导数是在卡普托（Caputo）意义下描述的。我们的主要目的是将勒让德（Legendre）运算矩阵推广到分数阶微积分。在这种方法中，截断的勒让德级数与分数阶导数的勒让德运算矩阵一起用于分数阶微分方程的数值积分。使用这种技术的方法背后的主要特点是，它将此类问题简化为求解代数方程组的问题，从而极大地简化了问题。该方法被应用于求解两种类型的分数阶微分方程，即线性和非线性的。文中包含了示例以证明所提出技术的有效性和适用性。（C）2009爱思唯尔有限公司。保留所有权利。
Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of a class of fractional differential equations. The fractional derivatives are described in the Caputo sense. Our main aim is to generalize the Legendre operational matrix to the fractional calculus. In this approach, a truncated Legendre series together with the Legendre operational matrix of fractional derivatives are used for numerical integration of fractional differential equations. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. (C) 2009 Elsevier Ltd. All rights reserved.