
Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2021, Volume 25, Number 2, Pages 241–256
(Mi vsgtu1820)




Differential Equations and Mathematical Physics
The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann–Liouville partial derivative
F. G. Khushtova^{} ^{} Institute of Applied Mathematics and Automation
of KabardinBalkar Scientific Centre of RAS,
Nal'chik, 360000, Russian Federation
Abstract:
The paper is devoted to the first boundaryvalue problem in a rectangular domain for a differential equation with the singular Bessel operator acting with respect to a spatial variable and the Riemann–Liouville fractional differentiation operator acting with respect to a time variable.
An explicit representation of the solution is constructed.
The uniqueness of the solution is proved in the class of functions satisfying the Hölder condition with respect to the time variable.
When the order of the fractional derivative is equal to unity, and the Bessel operator has no singularity, the studied equation coincides with the heat equation and the obtained results coincide with wellknown corresponding classical results.
Keywords:
fractional diffusion equation, fractional differentiation operator, Bessel operator, cylindrical function, Mittag–Leffler type function, first boundaryvalue problem
DOI:
https://doi.org/10.14498/vsgtu1820
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UDC:
517.95
MSC: 26A33, 35K20, 35R11 Received: August 18, 2020 Revised: May 18, 2021 Accepted: May 24, 2021 First online: June 30, 2021
Citation:
F. G. Khushtova, “The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann–Liouville partial derivative”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 25:2 (2021), 241–256
Citation in format AMSBIB
\Bibitem{Khu21}
\by F.~G.~Khushtova
\paper The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the RiemannLiouville partial derivative
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2021
\vol 25
\issue 2
\pages 241256
\mathnet{http://mi.mathnet.ru/vsgtu1820}
\crossref{https://doi.org/10.14498/vsgtu1820}
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