On Euler methods for Caputo fractional differential equations

Petr Tomášek

Archivum Mathematicum (2023)

  • Issue: 3, page 287-294
  • ISSN: 0044-8753

Abstract

top
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.

How to cite

top

Tomášek, Petr. "On Euler methods for Caputo fractional differential equations." Archivum Mathematicum (2023): 287-294. <http://eudml.org/doc/298989>.

@article{Tomášek2023,
abstract = {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.},
author = {Tomášek, Petr},
journal = {Archivum Mathematicum},
keywords = {Caputo derivative; numerical methods; initial value problem},
language = {eng},
number = {3},
pages = {287-294},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On Euler methods for Caputo fractional differential equations},
url = {http://eudml.org/doc/298989},
year = {2023},
}

TY - JOUR
AU - Tomášek, Petr
TI - On Euler methods for Caputo fractional differential equations
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 3
SP - 287
EP - 294
AB - 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.
LA - eng
KW - Caputo derivative; numerical methods; initial value problem
UR - http://eudml.org/doc/298989
ER -

References

top
  1. Diethelm, K., The analysis of fractional differential equations, Springer, Heidelberg, 2010. (2010) MR2680847
  2. Diethelm, K., 10.2478/s13540-011-0029-1, Fract. Calc. Appl. Anal. 84 (3) (2011), 475–490. (2011) MR2837642DOI10.2478/s13540-011-0029-1
  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. (2022) 
  4. Garrappa, R., Numerical solution of fractional differential equations: A survey and software tutorial, Mathematics 2018 (6) (2018), 1–23. (2018) MR3836966
  5. Garrappa, R., 10.1016/j.cnsns.2018.11.004, Commun. Nonlinear Sci. Numer. Simul. 70 (2019), 302–306. (2019) MR3874637DOI10.1016/j.cnsns.2018.11.004
  6. Li, C.P., Zeng, F.H., Numerical methods for fractional calculus, Chapman & Hall/CRC, Boca Raton, FL, 2015. (2015) MR3381791
  7. Podlubny, I., Fractional differential equations, Academic Press, San Diego, CA, 1999. (1999) 
  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. (2020) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.