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Time-fractional telegraph equation with ψ-Hilfer derivatives

2022-09Journal article Open access
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dc.contributor.authorVieira, Nelson
dc.contributor.authorFerreira, Milton
dc.contributor.authorRodrigues, M. Manuela
dc.date.accessioned2022-08-05T14:40:11Z
dc.date.available2024-09-01T00:30:22Z
dc.date.issued2022-09
dc.description.abstractThis paper deals with the investigation of the solution of the time-fractional telegraph equation in higher dimensions with $\psi$-Hilfer fractional derivatives. By application of the Fourier and $\psi$-Laplace transforms the solution is derived in closed form in terms of bivariate Mittag-Leffler functions in the Fourier domain and in terms of convolution integrals involving Fox H-functions of two-variables in the space-time domain. A double series representation of the first fundamental solution is deduced for the case of odd dimension. The results derived here are of general nature since our fractional derivatives allow to interpolate between Riemann-Liouville and Caputo fractional derivatives and the use of an arbitrary positive monotone increasing function $\psi$ in the kernel allows to encompass most of the fractional derivatives in the literature. In the one dimensional case, we prove the conditions under which the first fundamental solution of our equation can be interpreted as a spatial probability density function evolving in time, generalizing the results of Orsingher and Beghin (2004). Some plots of the fundamental solutions for different fractional derivatives are presented and analysed, and particular cases are addressed to show the consistency of our results.pt_PT
dc.description.versioninfo:eu-repo/semantics/acceptedVersionpt_PT
dc.identifier.citationN. Vieira, M. Ferreira, and M.M. Rodrigues, Time-fractional telegraph equation with psi-Hilfer derivatives, Chaos, Solitons & Fractals 162, Article 112276, 2022pt_PT
dc.identifier.doi10.1016/j.chaos.2022.112276pt_PT
dc.identifier.issn0960-0779
dc.identifier.urihttp://hdl.handle.net/10400.8/7514
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherElsevierpt_PT
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relation.ispartofseries112276;
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0960077922004866pt_PT
dc.subjectTime-fractional telegraph equationpt_PT
dc.subjectpsi-Hilfer fractional derivativept_PT
dc.subjectpsi-Laplace transformpt_PT
dc.subjectSeries and integral representationspt_PT
dc.subjectFractional momentspt_PT
dc.subjectProbability density functionpt_PT
dc.titleTime-fractional telegraph equation with ψ-Hilfer derivativespt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCenter for Research and Development in Mathematics and Applications
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT
oaire.citation.endPage26pt_PT
oaire.citation.startPage1pt_PT
oaire.citation.titleChaos, Solitons & Fractalspt_PT
oaire.citation.volume162pt_PT
oaire.fundingStream6817 - DCRRNI ID
person.familyNameVieira
person.familyNameFerreira
person.familyNameRodrigues
person.givenNameNelson
person.givenNameMilton
person.givenNameM. Manuela
person.identifier.ciencia-id9418-DDFB-DE9D
person.identifier.ciencia-idCA19-2009-F26D
person.identifier.ciencia-id461D-A5E2-23BE
person.identifier.orcid0000-0001-8756-4893
person.identifier.orcid0000-0003-1816-8293
person.identifier.orcid0000-0002-8834-5841
person.identifier.ridH-9130-2013
person.identifier.ridA-2004-2015
person.identifier.scopus-author-id55576073000
person.identifier.scopus-author-id12144179800
person.identifier.scopus-author-id22835991500
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.embargofctEmbargo da editora.pt_PT
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
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