Power functions and essentials of fractional calculus on isolated time scales

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F13%3APU104652" target="_blank" >RIV/00216305:26210/13:PU104652 - isvavai.cz</a>
Result on the web
<a href="https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-259" target="_blank" >https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-259</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1186/1687-1847-2013-259" target="_blank" >10.1186/1687-1847-2013-259</a>

Result language
angličtina
Original language name
Power functions and essentials of fractional calculus on isolated time scales
Original language description
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.
Czech name
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Czech description
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Project
<a href="/en/project/EE2.3.30.0039" target="_blank" >EE2.3.30.0039: Excellent young researcher at BUT</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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