2D-fractional Muntz–Legendre polynomials for solving the fractional partial differential equations

We present a numerical method for solving linear and nonlinear fractional partial differential equations (FPDEs) with variable coefficients. The main aim of the proposed method is to introduce an orthogonal basis of twodimensional fractional Muntz–Legendre polynomials. By using these polynomials, we approximate the unknown functions. Furthermore, an operational matrix of fractional derivative in the Caputo sense is provided for computing the fractional derivatives. The proposed approximation together with the Tau method reduces the solution of the FPDEs to the solution of a system of algebraic equations. Finally, to show the validity and accuracy of the presented method, we give some numerical examples.

Keywords:

Two-dimensional fractional Muntz–Legendre polynomials (2DFMLPs) , Fractional partial differential equations (FPDEs) , Operational matrix , Caputo fractional derivative