Effective Modified Fractional Reduced Differential Transform Method for Solving Multi-Term Time-Fractional Wave-Diffusion Equations

Abstract

In this work, we suggest a new method for solving linear multi-term time-fractional wave-diffusion equations, which is named the modified fractional reduced differential transform method (m-FRDTM). The importance of this technique is that it suggests a solution for a multi-term time-fractional equation. Very few techniques have been proposed to solve this type of equation, as will be shown in this paper. To show the effectiveness and efficiency of this proposed method, we introduce two different applications in two-term fractional differential equations. The three-dimensional and two-dimensional plots for different values of the fractional derivative are depicted to compare our results with the exact solutions.

Analyzing the Approximate Error and the Applicable Condition of Fractional Reduced Differential Transform Method

“…Similarly, fractional reduced differential transform method is also an approximate approach, and the approximate value is obtained by omitting some high order items of fractional expansions. It has been applied to solve fractional partial differential equations [17][18][19], higher-dimensional fractional equation [20], fractional nonlinear equation [21], fractional transport model [22], fractional financial models of awareness [23,24] etc. By this approach, the calculating process can be simplified and the approximate value can be drawn when the omitted high-order items are infinitesimal, but it can also mislead when the omitted high-order items are not infinitesimal.…”