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

In this paper, an iterative method for obtaining the numerical solutions of fractional partialdifferential equations (FPDEs) is introduced. This method is based on the combination of the differentialtransformation method (DTM) with fractional linear multistep methods (FLMM). The proposed methodhas a very low computational cost, with the help of which partial fractional differential equations areconverted into a system of ordinary differential equations. Then the resulting equations are solved with highaccuracy by applying fractional linear multi-step methods such as fractional Euler The series of solutionsobtained in the differential transformation method has a slow convergence speed in large regions. In thisstudy, 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 ofthe fractional differential equation. The obtained results confirm the proven stability and accuracy of themethod.