The Modified Fractional Power Series Method for Solving Fractional Non-isothermal Reaction–Diffusion Model Equations in a Spherical Catalyst

Abstract

In this paper, we study the fractional non-isothermal reaction–diffusion model equations in a spherical catalyst. The modified fractional power series method (MFPS) is employed to compute an approximation to the solution of this problem. The validity of the MFPS is ascertained by computing the solutions as \(\alpha \) approaches to 1 and comparing our results with other methods in the literature when \(\alpha =1\). The numerical results show the efficiency of our method. The existences of the solution is proved. In addition, the convergent of the proposed method is investigated. The influences of the main parameters in the model on the solution are discussed.