Publication detail

Power functions and essentials of fractional calculus on isolated time scales

KISELA, T.

Original Title

Power functions and essentials of fractional calculus on isolated time scales

Type

journal article - other

Language

English

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

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

Authors

KISELA, T.

RIV year

2013

Released

23. 8. 2013

Publisher

Springer

ISBN

1687-1847

Periodical

Advances in Difference Equations

Year of study

2013

Number

8

State

United States of America

Pages from

1

Pages to

18

Pages count

18

URL

https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-259

Full text in the Digital Library

http://hdl.handle.net/11012/137442

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"
}