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

Abstract EN

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.