Abstract and Applied Analysis

Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

Fukang Yin, Junqiang Song, Yongwen Wu, and Lilun Zhang

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Abstract

A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs). The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs). The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 562140, 13 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449997

Digital Object Identifier
doi:10.1155/2013/562140

Mathematical Reviews number (MathSciNet)
MR3129359

Zentralblatt MATH identifier
1291.65310

Citation

Yin, Fukang; Song, Junqiang; Wu, Yongwen; Zhang, Lilun. Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 562140, 13 pages. doi:10.1155/2013/562140. https://projecteuclid.org/euclid.aaa/1393449997


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