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.