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Time-fractional telegraph equation of distributed order in higher dimensions with Hilfer fractional derivatives

2022-07Journal article Open access
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dc.contributor.authorVieira, Nelson
dc.contributor.authorRodrigues, M. Manuela
dc.contributor.authorFerreira, Milton
dc.date.accessioned2022-08-24T10:36:25Z
dc.date.available2022-08-24T10:36:25Z
dc.date.issued2022-07
dc.description.abstractIn this paper, we consider time-fractional telegraph equations of distributed order in higher spatial dimensions, where the time derivatives are in the sense of Hilfer, thus interpolating between the Riemann-Liouville and the Caputo fractional derivatives. By employing the techniques of the Fourier, Laplace, and Mellin transforms, we obtain a representation of the solution of the Cauchy problem associated with the equation in terms of convolutions involving functions that are Laplace integrals of Fox H-functions. Fractional moments of the first fundamental solution are computed and for the special case of double-order distributed it is analyzed in detail the asymptotic behavior of the second-order moment, by application of the Tauberian Theorem. Finally, we exhibit plots of the variance showing its behavior for short and long times, and for different choices of the parameters along small dimensions.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationN. Vieira, M.M Rodrigues, and M. Ferreira, Time-fractional telegraph equation of distributed order in higher dimensions with Hilfer fractional derivatives, Electronic Research Archive 30(10), 2022, 3595-3631pt_PT
dc.identifier.doi10.3934/era.2022184pt_PT
dc.identifier.eissn2688-1594
dc.identifier.urihttp://hdl.handle.net/10400.8/7587
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherAIMS Presspt_PT
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relationNot Available
dc.relation.ispartofseries10;
dc.relation.publisherversionhttp://www.aimspress.com/article/doi/10.3934/era.2022184pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectTime-fractional telegraph equationpt_PT
dc.subjectDistributed orderpt_PT
dc.subjectHilfer fractional derivativept_PT
dc.subjectIntegral transformspt_PT
dc.subjectFox H-functionpt_PT
dc.subjectFractional momentspt_PT
dc.subjectTauberian Theorempt_PT
dc.titleTime-fractional telegraph equation of distributed order in higher dimensions with Hilfer fractional derivativespt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCenter for Research and Development in Mathematics and Applications
oaire.awardTitleNot Available
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/CEEC IND 2018/CEECIND%2F01131%2F2018%2FCP1559%2FCT0014/PT
oaire.citation.endPage3631pt_PT
oaire.citation.startPage3595pt_PT
oaire.citation.titleElectronic Research Archivept_PT
oaire.citation.volume30pt_PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStreamCEEC IND 2018
person.familyNameVieira
person.familyNameRodrigues
person.familyNameFerreira
person.givenNameNelson
person.givenNameM. Manuela
person.givenNameMilton
person.identifier.ciencia-id9418-DDFB-DE9D
person.identifier.ciencia-id461D-A5E2-23BE
person.identifier.ciencia-idCA19-2009-F26D
person.identifier.orcid0000-0001-8756-4893
person.identifier.orcid0000-0002-8834-5841
person.identifier.orcid0000-0003-1816-8293
person.identifier.ridH-9130-2013
person.identifier.ridA-2004-2015
person.identifier.scopus-author-id55576073000
person.identifier.scopus-author-id22835991500
person.identifier.scopus-author-id12144179800
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
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relation.isAuthorOfPublication57767487-249d-4111-a6c5-a22fed15d8ea
relation.isAuthorOfPublicationb1460cdc-4ced-46c6-a637-68b425d104dc
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