# Solving Fractional Partial Differential Equations Using Differential Transform Method Combined with Fractional Linear Multi-step Methods

Document Type : Original Paper

Authors

Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz„ Tabriz, Iran

Abstract

In this paper, an iterative method for obtaining the numerical solutions of fractional partial

differential equations (FPDEs) is introduced. This method is based on the combination of the differential

transformation method (DTM) with fractional linear multistep methods (FLMM). The proposed method

has a very low computational cost, with the help of which partial fractional differential equations are

converted into a system of ordinary differential equations. Then the resulting equations are solved with high

accuracy by applying fractional linear multi-step methods such as fractional Euler The series of solutions

obtained in the differential transformation method has a slow convergence speed in large regions. In this

study, by combining the mentioned method with linear multi-step methods, this shortcoming is solved.

Numerical results show that the obtained solutions. They are in good agreement with the exact solution of

the fractional differential equation. The obtained results confirm the proven stability and accuracy of the

method.

Keywords

Main Subjects

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### History

• Receive Date: 18 July 2022
• Revise Date: 06 January 2023
• Accept Date: 29 January 2023