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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1–10 (Mi semr892)  

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

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, MiklukhoMaklaya st., 6, Moscow, 117198, Russia
c Voronezh State University, Universitetskaya pl., 1, Voronezh, 394000, Russia

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 02.03.21.0008


DOI: https://doi.org/10.17377/semi.2018.15.001

Full text: PDF file (169 kB)
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Document Type: Article
UDC: 517.23, 517.518.126
MSC: 26A33, 44A15
Received October 19, 2017, published January 4, 2018

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Katrakhov, S. M. Sitnik, “Metod operatorov preobrazovaniya i kraevye zadachi dlya singulyarnykh ellipticheskikh uravnenii”, Singulyarnye differentsialnye uravneniya, SMFN, 64, no. 2, Rossiiskii universitet druzhby narodov, M., 2018, 211–426  mathnet  crossref
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