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

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  • Fukang Yin
  • Junqiang Song
  • Yongwen Wu
  • Lilun Zhang

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.

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:562140
DOI: 10.1155/2013/562140
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