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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 1–10
DOI: https://doi.org/10.17377/semi.2018.15.001 (Mi semr892) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Real, complex and functional analysis

On fractional powers of the Bessel operator on semiaxis

S. M. Sitnikab, E. L. Shishkinac

a Belgorod State National Research University, Pobeda st., 85, Belgorod, 308015, Russia
b RUDN University, Miklukho–Maklaya st., 6, Moscow, 117198, Russia
c Voronezh State University, Universitetskaya pl., 1, Voronezh, 394000, Russia
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DOI: https://doi.org/10.17377/semi.2018.15.001
Abstract: In this paper we study fractional powers of the Bessel differential operator defined on a semiaxis. Some important properties of such fractional powers of the Bessel differential operator are proved. They include connections with Legendre functions for kernel representations, fractional integral operators of Liouville and Saigo, Mellin transform and index laws. Possible applications are indicated to differential equations with fractional powers of the Bessel differential operator.
Keywords: Bessel operator, fractional integral, fractional derivative, Mellin transform.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.А03.21.0008
Received October 19, 2017, published January 4, 2018
Bibliographic databases:
Document Type: Article
UDC: 517.23, 517.518.126
MSC: 26A33, 44A15
Language: Russian
Citation: S. M. Sitnik, E. L. Shishkina, “On fractional powers of the Bessel operator on semiaxis”, Sib. Èlektron. Mat. Izv., 15 (2018), 1–10
Citation in format AMSBIB
\Bibitem{SitShi18}
\by S.~M.~Sitnik, E.~L.~Shishkina
\paper On fractional powers of the Bessel operator on semiaxis
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1--10
\mathnet{http://mi.mathnet.ru/semr892}
\crossref{https://doi.org/10.17377/semi.2018.15.001}
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