Power functions and essentials of fractional calculus on isolated time scales

Simple item page
dc.contributor.authorKisela, Tomášcs
dc.coverage.issue8cs
dc.coverage.volume2013cs
dc.date.issued2013-08-23cs
dc.description.abstractThis 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.en
dc.description.abstractThis 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.en
dc.formattextcs
dc.format.extent1-18cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationAdvances in Difference Equations. 2013, vol. 2013, issue 8, p. 1-18.en
dc.identifier.doi10.1186/1687-1847-2013-259cs
dc.identifier.issn1687-1847cs
dc.identifier.orcid0000-0002-9601-7071cs
dc.identifier.other101023cs
dc.identifier.researcheridE-2881-2013cs
dc.identifier.scopus35758804700cs
dc.identifier.urihttp://hdl.handle.net/11012/137442
dc.language.isoencs
dc.publisherSpringercs
dc.relation.ispartofAdvances in Difference Equationscs
dc.relation.urihttps://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-259cs
dc.rightsCreative Commons Attribution 2.0 Genericcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1687-1847/cs
dc.rights.urihttp://creativecommons.org/licenses/by/2.0/cs
dc.subjectfractional calculusen
dc.subjectpower functionsen
dc.subjecttime scalesen
dc.subjectconvolutionen
dc.subjectLaplace transformen
dc.subjectfractional calculus
dc.subjectpower functions
dc.subjecttime scales
dc.subjectconvolution
dc.subjectLaplace transform
dc.titlePower functions and essentials of fractional calculus on isolated time scalesen
dc.title.alternativePower functions and essentials of fractional calculus on isolated time scalesen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-101023en
sync.item.dbtypeVAVen
sync.item.insts2025.10.14 15:06:48en
sync.item.modts2025.10.14 10:39:08en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
168718472013259.pdf
Size:
460.17 KB
Format:
Adobe Portable Document Format
Description:
168718472013259.pdf
Download
Collections
Ústav matematiky