An Operator-Based Scheme for the Numerical Integration of FDEs

Inga Timofejeva, Zenonas Navickas, Tadas Telksnys, Romas Marcinkevicius and Minvydas Ragulskis
Additional contact information
Inga Timofejeva: Center for Nonlinear Systems, Kaunas University of Technology, Studentu, 50-147 Kaunas, Lithuania
Zenonas Navickas: Center for Nonlinear Systems, Kaunas University of Technology, Studentu, 50-147 Kaunas, Lithuania
Tadas Telksnys: Center for Nonlinear Systems, Kaunas University of Technology, Studentu, 50-147 Kaunas, Lithuania
Romas Marcinkevicius: Department of Software Engineering, Kaunas University of Technology, Studentu, 50-415 Kaunas, Lithuania
Minvydas Ragulskis: Center for Nonlinear Systems, Kaunas University of Technology, Studentu, 50-147 Kaunas, Lithuania

Mathematics, 2021, vol. 9, issue 12, 1-17

Abstract: An operator-based scheme for the numerical integration of fractional differential equations is presented in this paper. The generalized differential operator is used to construct the analytic solution to the corresponding characteristic ordinary differential equation in the form of an infinite power series. The approximate numerical solution is constructed by truncating the power series, and by changing the point of the expansion. The developed adaptive integration step selection strategy is based on the controlled error of approximation induced by the truncation. Computational experiments are used to demonstrate the efficacy of the proposed scheme.

Keywords: fractional differential equation; numerical integration; generalized differential operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/12/1372/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/12/1372/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:12:p:1372-:d:574462

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().