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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2015, Volume 19, Number 4, Pages 722–735
DOI: https://doi.org/10.14498/vsgtu1445
(Mi vsgtu1445)
 

This article is cited in 6 scientific papers (total in 6 papers)

Differential Equations and Mathematical Physics

Fundamental solution of the model equation of anomalous diffusion of fractional order

F. G. Khushtova

Institution of Applied Mathematics and Automation, Nal'chik, 360000, Russian Federation
Full-text PDF (785 kB) Citations (6)
(published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: Fundamental solution of the model equation of anomalous diffusion with Riemann–Liouville operator is constructed. Using the properties of the integral transformation with Wright function in kernel, we give estimates for the fundamental solution. When the considered equation transformes into the diffusion equation of fractional order, constructed fundamental solution goes into the corresponding fundamental solution of the diffusion equation of fractional order. General solution of the model equation of anomalous diffusion of fractional order is constructed.
Keywords: anomalous diffusion, diffusion fractional order, Riemann–Liouville operator, fundamental solution, general representation of solution, modified Bessel function, Wright function, integral transformation wich Wright function in kernel.
Original article submitted 15/VIII/2015
revision submitted – 19/X/2015
Bibliographic databases:
Document Type: Article
UDC: 517.968.7
Language: Russian
Citation: F. G. Khushtova, “Fundamental solution of the model equation of anomalous diffusion of fractional order”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:4 (2015), 722–735
Citation in format AMSBIB
\Bibitem{Khu15}
\by F.~G.~Khushtova
\paper Fundamental solution of the model equation of anomalous diffusion of fractional order
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 4
\pages 722--735
\mathnet{http://mi.mathnet.ru/vsgtu1445}
\crossref{https://doi.org/10.14498/vsgtu1445}
\zmath{https://zbmath.org/?q=an:06969190}
\elib{https://elibrary.ru/item.asp?id=25687499}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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