Superlinear solutions of sublinear fractional differential equations and regular variation

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dc.contributor.authorŘehák, Pavelcs
dc.coverage.issue1cs
dc.coverage.volume26cs
dc.date.issued2023-04-24cs
dc.description.abstractWe consider a sublinear fractional equation of the order in the interval (1, 2). We give conditions guaranteeing that this equation possesses asymptotically superlinear solutions. We show that all of these solutions are regularly varying and establish precise asymptotic formulae for them. Further we prove non-improvability of the conditions. In addition to the asymptotically superlinear solutions we discuss also other classes of solutions, some of them having no ODE analogy. In the very special case, when the coefficient is asymptotically equivalent to a power function and the order of the equation is 2, we get known results in their full generality. We reveal substantial differences between the integer order and non-integer order case. Among other tools, we utilize the fractional Karamata integration theorem and the fractional generalized L'Hospital rule which are proved in the paper. Several examples illustrating our results but serving also in alternative proofs are given too. We provide also numerical simulations.en
dc.formattextcs
dc.format.extent989-1015cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationFractional Calculus and Applied Analysis. 2023, vol. 26, issue 1, p. 989-1015.en
dc.identifier.doi10.1007/s13540-023-00156-1cs
dc.identifier.issn1311-0454cs
dc.identifier.orcid0000-0002-2452-2204cs
dc.identifier.other183583cs
dc.identifier.researcheridN-3315-2019cs
dc.identifier.scopus7102264947cs
dc.identifier.urihttp://hdl.handle.net/11012/213670
dc.language.isoencs
dc.publisherSpringer Naturecs
dc.relation.ispartofFractional Calculus and Applied Analysiscs
dc.relation.urihttps://link.springer.com/article/10.1007/s13540-023-00156-1cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1311-0454/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectSublinear fractional differential equationen
dc.subjectAsymptotically superlinear solutionen
dc.subjectRegularly varying functionen
dc.subjectKaramata theoremen
dc.subjectAsymptotic formulaen
dc.titleSuperlinear solutions of sublinear fractional differential equations and regular variationen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-183583en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:48:55en
sync.item.modts2025.01.17 16:50:36en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
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