Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

Abstract EN

A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs).

The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs).

The operational matrices of integration and derivative for 2D-FLFs are first derived.

Then, by these matrices, a system of algebraic equations is obtained from FPDEs.

Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed.

Three examples are discussed to demonstrate the validity and applicability of the proposed method.