Legendre polynomials operational matrix method for solving fractional partial differential equations with variable coefficients

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.