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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 1, Pages 74–84 (Mi vsgtu1455)  

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

Differential Equations and Mathematical Physics

Cauchy problem for a parabolic equation with Bessel operator and Riemann–Liouville partial derivative

F. G. Khushtova

Institute of Applied Mathematics and Automation, Nal'chik, 360000, Russian Federation

Abstract: In this paper Cauchy problem for a parabolic equation with Bessel operator and with Riemann–Liouville partial derivative is considered. The representation of the solution is obtained in terms of integral transform with Wright function in the kernel. It is shown that when this equation becomes the fractional diffusion equation, obtained solution becomes the solution of Cauchy problem for the corresponding equation. The uniqueness of the solution in the class of functions that satisfy the analogue of Tikhonov condition is proved.

Keywords: fractional calculus, Riemann–Liouville integral-differential operator, differential equations with partial fractional derivatives, parabolic equation, Bessel operator, the modified Bessel function of the first kind, Wright function, the integral transform with Wright function in the kernel, Fox $H$-function, Cauchy problem, Tikhonov condition

DOI: https://doi.org/10.14498/vsgtu1455

Full text: PDF file (701 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.968.7
MSC: 35A08, 35A22, 35R11, 35C15
Original article submitted 05/XI/2015
revision submitted – 07/II/2016

Citation: F. G. Khushtova, “Cauchy problem for a parabolic equation with Bessel operator and Riemann–Liouville partial derivative”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:1 (2016), 74–84

Citation in format AMSBIB
\Bibitem{Khu16}
\by F.~G.~Khushtova
\paper Cauchy problem for a parabolic equation with Bessel operator and Riemann--Liouville partial derivative
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 1
\pages 74--84
\mathnet{http://mi.mathnet.ru/vsgtu1455}
\crossref{https://doi.org/10.14498/vsgtu1455}
\zmath{https://zbmath.org/?q=an:06964474}
\elib{http://elibrary.ru/item.asp?id=26898117}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. F. G. Khushtova, “K probleme edinstvennosti resheniya zadachi Koshi dlya uravneniya drobnoi diffuzii s operatorom Besselya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:4 (2018), 774–784  mathnet  crossref  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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