Publication detail

Power functions and essentials of fractional calculus on isolated time scales

KISELA, T.

English title

Power functions and essentials of fractional calculus on isolated time scales

Type

Peer-reviewed article not indexed in WoS or Scopus

Language

en

Original abstract

This paper concerns with a recently suggested axiomatic definition of power functions on a general time scale and its consequences to fractional calculus. Besides a discussion of existence and uniqueness of such functions, we derive an efficient formula for the computation of power functions of rational orders on an arbitrary isolated time scale. It can be utilized in the introduction and evaluation of fractional sums and differences. We also deal with the Laplace transform of such fractional operators which, apart from solving of fractional difference equations, enables a more detailed comparison of our results with those in the relevant literature. Some illustrating examples (including special fractional initial value problems) are presented as well.

Keywords in English

fractional calculus; power functions; time scales; convolution; Laplace transform

Released

2013-08-23

Publisher

Springer

ISSN

1687-1847

Journal

Advances in Difference Equations

Volume

2013

Number

8

Pages from–to

1–18

Pages count

18

BIBTEX


@article{BUT101023,
  author="Tomáš {Kisela}",
  title="Power functions and essentials of fractional calculus on isolated time scales",
  journal="Advances in Difference Equations",
  year="2013",
  volume="2013",
  number="8",
  pages="1--18",
  doi="10.1186/1687-1847-2013-259",
  issn="1687-1847",
  url="https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-259"
}