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

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 op...

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Main Authors: Fukang Yin, Junqiang Song, Yongwen Wu, Lilun Zhang
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/562140
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author Fukang Yin
Junqiang Song
Yongwen Wu
Lilun Zhang
author_facet Fukang Yin
Junqiang Song
Yongwen Wu
Lilun Zhang
author_sort Fukang Yin
collection DOAJ
description 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.
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institution Kabale University
issn 1085-3375
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language English
publishDate 2013-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-1a3e9c49eb1c42769e97de0ed466be4f2025-02-03T01:10:56ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/562140562140Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre FunctionsFukang Yin0Junqiang Song1Yongwen Wu2Lilun Zhang3College of Computer, National University of Defense Technology, Changsha 410073, ChinaCollege of Computer, National University of Defense Technology, Changsha 410073, ChinaCollege of Computer, National University of Defense Technology, Changsha 410073, ChinaCollege of Computer, National University of Defense Technology, Changsha 410073, ChinaA 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.http://dx.doi.org/10.1155/2013/562140
spellingShingle Fukang Yin
Junqiang Song
Yongwen Wu
Lilun Zhang
Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
Abstract and Applied Analysis
title Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
title_full Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
title_fullStr Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
title_full_unstemmed Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
title_short Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
title_sort numerical solution of the fractional partial differential equations by the two dimensional fractional order legendre functions
url http://dx.doi.org/10.1155/2013/562140
work_keys_str_mv AT fukangyin numericalsolutionofthefractionalpartialdifferentialequationsbythetwodimensionalfractionalorderlegendrefunctions
AT junqiangsong numericalsolutionofthefractionalpartialdifferentialequationsbythetwodimensionalfractionalorderlegendrefunctions
AT yongwenwu numericalsolutionofthefractionalpartialdifferentialequationsbythetwodimensionalfractionalorderlegendrefunctions
AT lilunzhang numericalsolutionofthefractionalpartialdifferentialequationsbythetwodimensionalfractionalorderlegendrefunctions