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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2016, Volume 20, Number 4, Pages 603–619 (Mi vsgtu1520)  

This article is cited in 2 scientific papers (total in 2 papers)

Differential Equations and Mathematical Physics

An approximate group classification of a perturbed subdiffusion equation

S. Yu. Lukashchuk

Ufa State Aviation Technical University, Ufa, 450000, Russian Federation

Abstract: A problem of the Lie point approximate symmetry group classification of a perturbed subdiffusion equation with a small parameter is solved. The classification is performed with respect to anomalous diffusion coefficient which is considered as a function of an independent variable. The perturbed subdiffusion equation is derived from a fractional subdiffusion equation with the Riemann-Liouville time-fractional derivative under an assumption that the order of fractional differentiation is close to unity. As it is follow from the classification results, the perturbed subdiffusion equation admits a more general Lie point symmetry group than the initial fractional subdiffusion equation. The obtained results permit to construct approximate invariant solutions for the perturbed subdiffusion equation corresponding to different functions of the anomalous diffusion coefficient. These solutions will also be the approximate solutions of the initial fractional subdiffusion equation.

Keywords: fractional differential equation, subdiffusion, small parameter, approximate transformation group, group classification.

DOI: https://doi.org/10.14498/vsgtu1520

Full text: PDF file (860 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.958:[536.2+539.219.3]
MSC: 35R11, 35B20, 70G65
Original article submitted 27/X/2016
revision submitted – 12/XI/2016

Citation: S. Yu. Lukashchuk, “An approximate group classification of a perturbed subdiffusion equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:4 (2016), 603–619

Citation in format AMSBIB
\Bibitem{Luk16}
\by S.~Yu.~Lukashchuk
\paper An approximate group classification of a perturbed subdiffusion equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 4
\pages 603--619
\mathnet{http://mi.mathnet.ru/vsgtu1520}
\crossref{https://doi.org/10.14498/vsgtu1520}
\zmath{https://zbmath.org/?q=an:06964658}
\elib{https://elibrary.ru/item.asp?id=28862957}


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    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. S. Yu. Lukaschuk, “Priblizhenie obyknovennykh drobno-differentsialnykh uravnenii differentsialnymi uravneniyami s malym parametrom”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 515–531  mathnet  crossref  elib
    2. S. Yu. Lukashchuk, “Approximate conservation laws for fractional differential equations”, Commun. Nonlinear Sci. Numer. Simul., 68 (2019), 147–159  crossref  mathscinet  isi  scopus
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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