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Mathematical Problems in Engineering
Volume 2015, Article ID 915195, 9 pages
Research Article

Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients

School of Aeronautic Science and Technology, Beihang University, Beijing 100191, China

Received 27 January 2015; Accepted 4 May 2015

Academic Editor: Francesco Pesavento

Copyright © 2015 Yongqiang Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A numerical method for solving a class of fractional partial differential equations with variable coefficients based on Legendre polynomials is proposed. A fractional order operational matrix of Legendre polynomials is also derived. The initial equations are transformed into the products of several matrixes by using the operational matrix. A system of linear equations is obtained by dispersing the coefficients and the products of matrixes. Only a small number of Legendre polynomials are needed to acquire a satisfactory result. Results obtained using the scheme presented here show that the numerical method is very effective and convenient for solving fractional partial differential equations with variable coefficients.