Detail publikace

Power functions and essentials of fractional calculus on isolated time scales

KISELA, T.

Originální název

Power functions and essentials of fractional calculus on isolated time scales

Typ

článek v časopise - ostatní, Jost

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

KISELA, T.

Rok RIV

2013

Vydáno

23. 8. 2013

Nakladatel

Springer

ISSN

1687-1847

Periodikum

Advances in Difference Equations

Ročník

2013

Číslo

8

Stát

Spojené státy americké

Strany od

1

Strany do

18

Strany počet

18

URL

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

Plný text v Digitální knihovně

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"
}