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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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UDC: 517.23, 517.518.126 MSC: 26A33, 44A15 Received Citation: S. M. Sitnik, E. L. Shishkina, “On fractional powers of the Bessel operator on semiaxis”, Sib. Èlektron. Mat. Izv., 15 (2018), 
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