Abstract
We give an efficient numerical approach to solve variable-order fractional differential equations (VO-FDEs) by applying fractional-order generalized Chelyshkov wavelets (FOGCW). The beta function is used to determine the exact value for the Riemann-Liouville fractional integral operator of the FOGCW. The exact value and the given wavelets are used to solve the VO-FDEs. Six examples are included to demonstrate the effectiveness of this method. In the last example, we show the application of our method to the variable-order fractional relaxation model.
| Original language | English |
|---|---|
| Pages (from-to) | 1571-1588 |
| Number of pages | 18 |
| Journal | Numerical Algorithms |
| Volume | 92 |
| Issue number | 3 |
| Early online date | 8 Aug 2022 |
| DOIs | |
| Publication status | Published - 31 Mar 2023 |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Acknowledgements
The author would like to thank the VIASM for providing a fruitful research environment and extending support and hospitality during their visit. The authors wish to express their sincere thanks to the anonymous referee for valuable suggestions that improved the final version of the manuscript.Funding
A part of this paper was completed when the corresponding author was working as a researcher at Vietnam Institute for Advance Study in Mathematics (VIASM).
Keywords
- Chelyshkov wavelet
- Fractional differential equation
- Fractional-order
- Relaxation system
- Variable-order
ASJC Scopus subject areas
- Applied Mathematics