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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 11, Pages 38–51
DOI: https://doi.org/10.26907/0021-3446-2022-11-38-51 (Mi ivm9827) 		 
A finite difference scheme on a graded mesh for solving Cauchy problems with a fractional Caputo derivative in a Banach space

M. M. Kokurina, S. I. Piskarevba

a Mari State University, 1 Lenin sqr., Yoshkar-Ola, 424001 Russia
b Moscow State University, 1 Leninskie Gory, Moscow, 119234 Russia
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DOI: https://doi.org/10.26907/0021-3446-2022-11-38-51
Abstract: We study a well-posed Cauchy problem with a fractional Caputo derivative of the order $\alpha\in(0,1)$ in a Banach space. We build and explore a finite difference scheme on a graded mesh for solving such problems. The stability and accuracy estimates for a proposed finite difference scheme are obtained.
Keywords: Cauchy problem, Caputo derivative, Banach space, finite difference scheme, stability, accuracy estimate, graded mesh, full discretization.
Funding agency Grant number
Russian Science Foundation 20-11-20085
Received: 14.01.2022
Revised: 20.04.2022
Accepted: 29.06.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 11, Pages 33–45
DOI: https://doi.org/10.3103/S1066369X22110044
Document Type: Article
UDC: 517.983: 517.968: 519.642
Language: Russian
Citation: M. M. Kokurin, S. I. Piskarev, “A finite difference scheme on a graded mesh for solving Cauchy problems with a fractional Caputo derivative in a Banach space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 11, 38–51; Russian Math. (Iz. VUZ), 66:11 (2022), 33–45
Citation in format AMSBIB
\Bibitem{KokPis22}
\by M.~M.~Kokurin, S.~I.~Piskarev
\paper A finite difference scheme on a graded mesh for solving Cauchy problems with a fractional Caputo derivative in a Banach space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 11
\pages 38--51
\mathnet{http://mi.mathnet.ru/ivm9827}
\crossref{https://doi.org/10.26907/0021-3446-2022-11-38-51}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 11
\pages 33--45
\crossref{https://doi.org/10.3103/S1066369X22110044}
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