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Article

An Operator-Based Scheme for the Numerical Integration of FDEs

1
Center for Nonlinear Systems, Kaunas University of Technology, Studentu, 50-147 Kaunas, Lithuania
2
Department of Software Engineering, Kaunas University of Technology, Studentu, 50-415 Kaunas, Lithuania
*
Author to whom correspondence should be addressed.
Academic Editors: Charampos Tsitouras and Theodore E. Simos
Mathematics 2021, 9(12), 1372; https://doi.org/10.3390/math9121372
Received: 24 May 2021 / Revised: 9 June 2021 / Accepted: 10 June 2021 / Published: 13 June 2021
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)
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. View Full-Text
Keywords: fractional differential equation; numerical integration; generalized differential operator fractional differential equation; numerical integration; generalized differential operator
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MDPI and ACS Style

Timofejeva, I.; Navickas, Z.; Telksnys, T.; Marcinkevicius, R.; Ragulskis, M. An Operator-Based Scheme for the Numerical Integration of FDEs. Mathematics 2021, 9, 1372. https://doi.org/10.3390/math9121372

AMA Style

Timofejeva I, Navickas Z, Telksnys T, Marcinkevicius R, Ragulskis M. An Operator-Based Scheme for the Numerical Integration of FDEs. Mathematics. 2021; 9(12):1372. https://doi.org/10.3390/math9121372

Chicago/Turabian Style

Timofejeva, Inga, Zenonas Navickas, Tadas Telksnys, Romas Marcinkevicius, and Minvydas Ragulskis. 2021. "An Operator-Based Scheme for the Numerical Integration of FDEs" Mathematics 9, no. 12: 1372. https://doi.org/10.3390/math9121372

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