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Eigenfunctions of the time‐fractional diffusion‐wave operator

2020-12-06Journal article Open access
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dc.contributor.authorFerreira, M.
dc.contributor.authorLuchko, Yu.
dc.contributor.authorRodrigues, M. M.
dc.contributor.authorVieira, N.
dc.date.accessioned2021-03-18T17:20:06Z
dc.date.available2021-12-01T01:30:15Z
dc.date.issued2020-12-06
dc.description.abstractIn this paper, we present some new integral and series representations for the eigenfunctions of the multidimensional time-fractional diffusion-wave operator with the time-fractional derivative of order $\beta \in ]1,2[$ defined in the Caputo sense. The integral representations are obtained in form of the inverse Fourier-Bessel transform and as double contour integrals of the Mellin-Barnes type. Concerning series expansions, the eigenfunctions are expressed as the double generalized hypergeometric series for any $\beta \in ]1,2[$ and as Kamp\'{e} de F\'{e}riet and Lauricella series in two variables for the rational values of $\beta$. The limit cases $\beta=1$ (diffusion operator) and $\beta=2$ (wave operator) as well as an intermediate case $\beta=\frac{3}{2}$ are studied in detail. Finally, we provide several plots of the eigenfunctions to some selected eigenvalues for different particular values of the fractional derivative order $\beta$ and the spatial dimension $n$.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationFerreira, M., Luchko, Yu., Rodrigues, M.M., Vieira, N., Eigenfunctions of the time‐fractional diffusion‐wave operator. Math Meth Appl Sci. 2021; 44(2): 1713–1743. https://doi.org/10.1002/mma.6874pt_PT
dc.identifier.doihttps://doi.org/10.1002/mma.6874pt_PT
dc.identifier.issn0170-4214
dc.identifier.issn1099-1476
dc.identifier.urihttp://hdl.handle.net/10400.8/5523
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherWiley Online Librarypt_PT
dc.relationNot Available
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relation.publisherversionhttps://onlinelibrary.wiley.com/doi/10.1002/mma.6874pt_PT
dc.subjectTime-fractional diffusion-wave operator Eigenfunctions; Caputo fractional derivatives; Generalized hypergeometric series.pt_PT
dc.subjectEigenfunctionspt_PT
dc.subjectCaputo fractional derivativespt_PT
dc.subjectGeneralized hypergeometric seriespt_PT
dc.titleEigenfunctions of the time‐fractional diffusion‐wave operatorpt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleNot Available
oaire.awardTitleCenter for Research and Development in Mathematics and Applications
oaire.awardTitleCenter for Research and Development in Mathematics and Applications
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/CEEC IND 2018/CEECIND%2F01131%2F2018%2FCP1559%2FCT0014/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04106%2F2020/PT
oaire.citation.endPage1743pt_PT
oaire.citation.issue2pt_PT
oaire.citation.startPage1713pt_PT
oaire.citation.titleMathematical Methods in the Applied Sciencespt_PT
oaire.citation.volume44pt_PT
oaire.fundingStreamCEEC IND 2018
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
person.familyNameFerreira
person.familyNameRodrigues
person.familyNameVieira
person.givenNameMilton
person.givenNameM. Manuela
person.givenNameNelson
person.identifier.ciencia-idCA19-2009-F26D
person.identifier.ciencia-id461D-A5E2-23BE
person.identifier.ciencia-id9418-DDFB-DE9D
person.identifier.orcid0000-0003-1816-8293
person.identifier.orcid0000-0002-8834-5841
person.identifier.orcid0000-0001-8756-4893
person.identifier.ridA-2004-2015
person.identifier.ridH-9130-2013
person.identifier.scopus-author-id12144179800
person.identifier.scopus-author-id22835991500
person.identifier.scopus-author-id55576073000
project.funder.identifierhttp://doi.org/10.13039/501100001871
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
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
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