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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2015, Volume 19, Number 1, Pages 78–86 (Mi vsgtu1398)  

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

Differential Equations and Mathematical Physics

Nonlocal problem for partial differential equations of fractional order

O. A. Repinab, A. V. Tarasenkoc

a Samara State University of Economics, Samara, 443090, Russian Federation
b Samara State Technical University, Samara, 443100, Russian Federation
c Samara State University of Architecture and Construction, Samara, 443001, Russian Federation

Abstract: A nonlocal problem is investigated for the partial differential equation (diffusion equation of fractional order) in a finite domain. The boundary condition contains a linear combination of generalized operators of fractional integro-differentiation used on the solution in the characteristics and the solution and its derivative in the degenerating line. The uniqueness of the solution is proved by a modified Tricomi method. The existence of the solution is equivalently reduced to the question of the solvability of Fredholm integral equations of the second kind.

Keywords: operator of fractional integro-differentiation, boundary value problem, Fredholm integral equation of the second kind

DOI: https://doi.org/10.14498/vsgtu1398

Full text: PDF file (705 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.956.6
MSC: 35M12
Original article submitted 05/XI/2014
revision submitted – 11/I/2015

Citation: O. A. Repin, A. V. Tarasenko, “Nonlocal problem for partial differential equations of fractional order”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:1 (2015), 78–86

Citation in format AMSBIB
\Bibitem{RepTar15}
\by O.~A.~Repin, A.~V.~Tarasenko
\paper Nonlocal problem for partial differential equations 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 1
\pages 78--86
\mathnet{http://mi.mathnet.ru/vsgtu1398}
\crossref{https://doi.org/10.14498/vsgtu1398}
\zmath{https://zbmath.org/?q=an:06968949}
\elib{https://elibrary.ru/item.asp?id=23681743}


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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. A. V. Tarasenko, “On solvability of nonlocal problem for loaded parabolic-hyperbolic equation”, Russian Math. (Iz. VUZ), 62:3 (2018), 53–59  mathnet  crossref  isi
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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