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

Abstract

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The obtained result is the approximation of the real value. Currently, there are few reports on the approximate error and applicable condition. In this paper, we study the factors related to the approximate errors according to the fractional expansions. Our research shows that the approximate errors relate not only to fractional order but also to time t, and that they increase rapidly with time t. This method can only be applied within a certain time range, and the time range is relevant to fractional order and fractional expansions. We can ascertain this time range according to the absolute error and the relative error. Many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis.