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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1–10
(Mi semr892)
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This article is cited in 3 scientific papers (total in 3 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
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.
DOI:
https://doi.org/10.17377/semi.2018.15.001
Full text:
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Bibliographic databases:
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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http://mi.mathnet.ru/eng/semr892 http://mi.mathnet.ru/eng/semr/v15/p1
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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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
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E. L. Shishkina, “Obschee uravnenie Eilera—Puassona—Darbu i giperbolicheskie $B$-potentsialy”, Uravneniya v chastnykh proizvodnykh, SMFN, 65, no. 2, Rossiiskii universitet druzhby narodov, M., 2019, 157–338
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E. Shishkina, S. Sitnik, “A fractional equation with left-sided fractional Bessel derivatives of Gerasimov-Caputo type”, Mathematics, 7:12 (2019), 1216
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