Polynomial Approximation Method For Solving Fractional Partial Differential Equations

Abstract

This paper presents a modern approach for solving fractional partial

differential equations (FPDE) which is called the polynomial

approximation method based on the polynomial approximation

and on its general fractional derivative formula. By modifying the general

fractional derivative formula of and with the aid of the linear

FPDE, another new formula can be found for the approximation .

This is the basic idea of the proposed method. Furthermore, the

mathematical proof of the convergence and stability of this method have

been studied. Some numerical examples show that the proposed method

exhibits a satisfactory results.