Chebyshev polynomials for approximation of solution of fractional partial differential equations with variable coefficients

摘要

In this paper, a numerical method for solving a class of fractional partial differential equations with variable coefficients based on Chebyshev polynomials is proposed. The fractional derivative is described in the Caputo sense. The properties of Chebyshev polynomials are used to reduce the initial equations to the products of several matrixes. A system of linear equations are obtained by dispersing the coefficients and the products of matrixes. Only a small number of Chebyshev 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.