| Title:
|
On Euler methods for Caputo fractional differential equations (English) |
| Author:
|
Tomášek, Petr |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2023 |
| Pages:
|
287-294 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Numerical methods for fractional differential equations have specific properties with respect to the ones for ordinary differential equations. The paper discusses Euler methods for Caputo differential equation initial value problem. The common properties of the methods are stated and demonstrated by several numerical experiments. Python codes are available to researchers for numerical simulations. (English) |
| Keyword:
|
Caputo derivative |
| Keyword:
|
numerical methods |
| Keyword:
|
initial value problem |
| MSC:
|
26A33 |
| MSC:
|
34A08 |
| MSC:
|
65L05 |
| idZBL:
|
Zbl 07675598 |
| idMR:
|
MR4563040 |
| DOI:
|
10.5817/AM2023-3-287 |
| . |
| Date available:
|
2023-02-22T14:58:38Z |
| Last updated:
|
2023-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151576 |
| . |
| Reference:
|
[1] Diethelm, K.: The analysis of fractional differential equations.Springer, Heidelberg, 2010. MR 2680847 |
| Reference:
|
[2] Diethelm, K.: An efficient parallel algorithm for the numerical solution of fractional differential equations.Fract. Calc. Appl. Anal. 84 (3) (2011), 475–490. MR 2837642, 10.2478/s13540-011-0029-1 |
| Reference:
|
[3] Diethelm, K., Kiryakova, V., Luchko, Y., Machado, J.A.T., Tarasov, V.E.: Trends, directions for further research, and some open problems of fractional calculus.Nonlinear Dyn. 107 (2022), 3245–3270. |
| Reference:
|
[4] Garrappa, R.: Numerical solution of fractional differential equations: A survey and software tutorial.Mathematics 2018 (6) (2018), 1–23. MR 3836966 |
| Reference:
|
[5] Garrappa, R.: Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations.Commun. Nonlinear Sci. Numer. Simul. 70 (2019), 302–306. MR 3874637, 10.1016/j.cnsns.2018.11.004 |
| Reference:
|
[6] Li, C.P., Zeng, F.H.: Numerical methods for fractional calculus.Chapman & Hall/CRC, Boca Raton, FL, 2015. MR 3381791 |
| Reference:
|
[7] Podlubny, I.: Fractional differential equations.Academic Press, San Diego, CA, 1999. |
| Reference:
|
[8] Rosu, F.: Parallel algorithm for numerical methods applied to fractional-order system.Parallel algorithm for numerical methods applied to fractional-order system 21 (4) (2020), 701–707. |
| . |
