This paper presents a new method for solving fractional partial differential equations (FPDE) which is called the polynomial approximation method based on the polynomial approximation uN(x,t) and on its general fractional derivative formula.By modifying the general fractional derivative formula of uN(x,t) and with the aid of the linear FPDE, another new formula can be found for the approximation uN(x,t). 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.
