Version 1
: Received: 16 May 2024 / Approved: 17 May 2024 / Online: 17 May 2024 (15:27:43 CEST)
How to cite:
Hu, J. Analyzing the Approximate Error and the Applicable Condition of Fractional Reduced Differential Transform Method. Preprints2024, 2024051168. https://doi.org/10.20944/preprints202405.1168.v1
Hu, J. Analyzing the Approximate Error and the Applicable Condition of Fractional Reduced Differential Transform Method. Preprints 2024, 2024051168. https://doi.org/10.20944/preprints202405.1168.v1
Hu, J. Analyzing the Approximate Error and the Applicable Condition of Fractional Reduced Differential Transform Method. Preprints2024, 2024051168. https://doi.org/10.20944/preprints202405.1168.v1
APA Style
Hu, J. (2024). Analyzing the Approximate Error and the Applicable Condition of Fractional Reduced Differential Transform Method. Preprints. https://doi.org/10.20944/preprints202405.1168.v1
Chicago/Turabian Style
Hu, J. 2024 "Analyzing the Approximate Error and the Applicable Condition of Fractional Reduced Differential Transform Method" Preprints. https://doi.org/10.20944/preprints202405.1168.v1
Abstract
The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The result obtained is the approximation of the real value. There are few reports on the approximate error and the applicable condition. In this paper, according to the fractional expansions, we study the factors related to the approximate errors. Our research shows that the approximate errors relate not only to fractional order but also to time $t$ and 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. Then, many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
