Ufimskii Matematicheskii Zhurnal
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Ufimsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 Ufimsk. Mat. Zh., 2019, Volume 11, Issue 2, Pages 19–35 (Mi ufa469)

Difference schemes for partial differential equations of fractional order

A. K. Bazzaevab, I. D. Tsopanovb

a Khetagurov North-Ossetia State University, Vatutina str., 44-46, 362025, Vladikavkaz, Russia

Abstract: Nowadays, fractional differential equations arise while describing physical systems with such properties as power nonlocality, long-term memory and fractal property. The order of the fractional derivative is determined by the dimension of the fractal. Fractional mathematical calculus in the theory of fractals and physical systems with memory and non-locality becomes as important as classical analysis in continuum mechanics.
In this paper we consider higher order difference schemes of approximation for differential equations with fractional-order derivatives with respect to both spatial and time variables. Using the maximum principle, we obtain apriori estimates and prove the stability and the uniform convergence of difference schemes.

Keywords: initial-boundary value problem, fractional differential equations, Caputo fractional derivative, stability, slow diffusion equation, difference scheme, maximum principle, stability, uniform convergence, apriori estimate, heat capacity concentrated at the boundary.

Full text: PDF file (473 kB)
References: PDF file   HTML file

English version:
Ufa Mathematical Journal, 2019, 11:2, 19–33 (PDF, 404 kB); https://doi.org/10.13108/2019-11-2-19

Bibliographic databases:

UDC: 519.633
MSC: 65M12

Citation: A. K. Bazzaev, I. D. Tsopanov, “Difference schemes for partial differential equations of fractional order”, Ufimsk. Mat. Zh., 11:2 (2019), 19–35; Ufa Math. J., 11:2 (2019), 19–33

Citation in format AMSBIB
\Bibitem{BazTso19} \by A.~K.~Bazzaev, I.~D.~Tsopanov \paper Difference schemes for partial differential equations of fractional order \jour Ufimsk. Mat. Zh. \yr 2019 \vol 11 \issue 2 \pages 19--35 \mathnet{http://mi.mathnet.ru/ufa469} \transl \jour Ufa Math. J. \yr 2019 \vol 11 \issue 2 \pages 19--33 \crossref{https://doi.org/10.13108/2019-11-2-19} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000511171600002} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85078655530} 

• http://mi.mathnet.ru/eng/ufa469
• http://mi.mathnet.ru/eng/ufa/v11/i2/p19

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. I. Vasilev, A. M. Kardashevskii, “Iteratsionnaya identifikatsiya koeffitsienta diffuzii v nachalno-kraevoi zadache dlya uravneniya subdiffuzii”, Sib. zhurn. industr. matem., 24:2 (2021), 23–37
•  Number of views: This page: 265 Full text: 211 References: 19