On fractional powers of the Bessel operator on semiaxis

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. © 2018 Sitnik SM, Shishkina EL.

Authors
Sitnik S.M. 1, 2 , Shishkina E.L.3
Publisher
Sobolev Institute of Mathematics
Language
English
Pages
1-10
Status
Published
Volume
15
Year
2018
Organizations
  • 1 Belgorod State National Research University, Pobeda st., 85, Belgorod, 308015, Russian Federation
  • 2 RUDN University, Miklukho-Maklaya st., 6, Moscow, 117198, Russian Federation
  • 3 Voronezh State University, Universitetskaya pl., 1, Voronezh, 394000, Russian Federation
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/7248/