Abstract
In this paper, we propose a numerical method for solving distributed-order fractional partial differential equations (FPDEs). For this method, we first introduce fractional-order generalized Taylor wavelets (FOGTW). An estimation for the error of the approximation is also studied. In addition, by using the regularized beta function we give a formula for determining the Riemann-Liouville fractional integral operator for the FOGTW. Combining this formula with the Gauss-Legendre quadrature, we obtain a numerical method for solving distributed-order FPDEs. Several illustrative examples are given to show the applicability and the accuracy of the proposed method.
| Original language | English |
|---|---|
| Pages (from-to) | 349-367 |
| Number of pages | 19 |
| Journal | Applied Numerical Mathematics |
| Volume | 160 |
| Early online date | 21 Oct 2020 |
| DOIs | |
| Publication status | Published - 28 Feb 2021 |
Bibliographical note
Publisher Copyright:© 2020 IMACS
Acknowledgements
The authors wish to express their sincere thanks to the anonymous referee for valuable suggestions that improved the final version of the manuscript.Keywords
- Distributed-order differential equation
- Fractional partial differential equation
- Numerical method
- Numerical solution
- Taylor wavelet
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics