Geodesic
On fractional powers of the Bessel operator on semiaxis
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1-10

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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. 
@article{SEMR_2018_15_a120,
     author = {S. M. Sitnik and E. L. Shishkina},
     title = {On fractional powers of the {Bessel} operator on semiaxis},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1--10},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a120/}
}
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S. M. Sitnik; E. L. Shishkina. On fractional powers of the Bessel operator on semiaxis. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1-10. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a120/