English

On fractional powers of the Bessel operator on a semiaxis

Classical Analysis and ODEs 2018-06-04 v2

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

Cite

@article{arxiv.1706.01928,
  title  = {On fractional powers of the Bessel operator on a semiaxis},
  author = {S. M. Sitnik and E. L. Shishkina},
  journal= {arXiv preprint arXiv:1706.01928},
  year   = {2018}
}

Comments

English version (pp. 1--8) and Russian version (pp. 9--18)