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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 1078–1098
DOI: https://doi.org/10.17377/semi.2016.13.086
(Mi semr736)
 

This article is cited in 18 scientific papers (total in 18 papers)

Differentical equations, dynamical systems and optimal control

Fractional diffusion equation with discretely distributed differentiation operator

A. V. Pskhu

Institute of Applied Mathematics and Automation, Shortanova street, 9A, 360000, Nalchik, Russia
References:
Abstract: We discuss an initial value problem for a fractional diffusion equation with discretely distributed fractional differentiation operator with respect to time variable. We construct a fundamental solution of the considered equation, give a solution of the problem under study, and prove a uniqueness theorem in the class of rapid growth functions. The fractional differentiation is given by the Dzhrbashyan–Nersesyan operator, and the corresponding results for equations with Caputo and Riemann–Liouville derivatives are particular cases of proved assertions.
Keywords: fractional diffusion equation, Cauchy problem, fractional derivative, discretely distributed fractional differentiation operator, multi-term fractional diffusion equation, Dzhrbashyan–Nersesyan fractional differentiation operator, Riemann–Liouville derivative, Caputo derivative, Tychonoff condition, Wright function.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00462_а
Received July 17, 2016, published December 14, 2016
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35R11
Language: Russian
Citation: A. V. Pskhu, “Fractional diffusion equation with discretely distributed differentiation operator”, Sib. Èlektron. Mat. Izv., 13 (2016), 1078–1098
Citation in format AMSBIB
\Bibitem{Psk16}
\by A.~V.~Pskhu
\paper Fractional diffusion equation with discretely distributed differentiation operator
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 1078--1098
\mathnet{http://mi.mathnet.ru/semr736}
\crossref{https://doi.org/10.17377/semi.2016.13.086}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3580054}
\zmath{https://zbmath.org/?q=an:1370.35268}
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  • https://www.mathnet.ru/eng/semr/v13/p1078
  • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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