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

Fukang Yin | Zendy; Junqiang Song | Zendy; Yongwen Wu | Zendy; Lilun Zhang | Zendy

Open Access

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

Author(s) -

Fukang Yin,

Junqiang Song,

Yongwen Wu,

Lilun Zhang

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/562140

Subject(s) - mathematics , legendre polynomials , fractional calculus , algebraic equation , mathematical analysis , partial derivative , order (exchange) , partial differential equation , legendre function , legendre wavelet , nonlinear system , discrete wavelet transform , physics , wavelet transform , finance , quantum mechanics , artificial intelligence , computer science , wavelet , economics

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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