## Abstract and Applied Analysis

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

### 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

**Full-text: Open access**

#### 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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