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

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Hengamian Asl E.; Saberi Nadjafi J.; Gachpazan M.

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2020 | Volume:10 | Issue:2 Page(s): 1-31

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Information Journal Paper

Title

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

Author(s)

Hengamian Asl E. | Saberi Nadjafi J. | Gachpazan M. | Issue Writer Certificate

Keywords

Two-dimensional fractional Muntz–Legendre polynomials (2DFMLPs)

Fractional partial differential equations (FPDEs)

Operational matrix

Caputo fractional derivative

Abstract

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.

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