Abstract
This paper aims to provide a new numerical method for solving variable-order fractional diffusion equations. The method is constructed using fractional-order Taylor wavelets. By using the regularized beta function, a formula for computing the exact value of Riemann-Liouville fractional integral operator of the fractional-order Taylor wavelets is given. The Taylor wavelets properties and the formula are used in combination with a spectral collocation method to reduce the given diffusion equation to a system of algebraic equations. The method is easy to implement, and gives very accurate solutions. Several examples are given to show the applicability and the effectiveness of the method.
| Original language | English |
|---|---|
| Pages (from-to) | 2668-2686 |
| Number of pages | 19 |
| Journal | Numerical Methods for Partial Differential Equations |
| Volume | 37 |
| Issue number | 3 |
| Early online date | 23 Mar 2021 |
| DOIs | |
| Publication status | Published - 31 May 2021 |
Bibliographical note
Publisher Copyright:© 2021 Wiley Periodicals LLC
Keywords
- diffusion equations
- fractional partial differential equation
- fractional-order
- regularized beta function
- Taylor wavelet
- variable-order
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics