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

This article is cited in 1 scientific paper (total in 1 paper)

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
b Vladikavkaz Administration Institute, Borodinskaya str., 14, 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.

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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
Received: 31.05.2018

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
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\paper Difference schemes for partial differential equations of fractional order
\jour Ufimsk. Mat. Zh.
\yr 2019
\vol 11
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\pages 19--35
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\jour Ufa Math. J.
\yr 2019
\vol 11
\issue 2
\pages 19--33
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    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  mathnet  crossref
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