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Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives

dc.contributor.authorFerreira, Milton
dc.contributor.authorVieira, Nelson Felipe Loureiro
dc.date.accessioned2019-02-07T14:25:01Z
dc.date.available2019-02-07T14:25:01Z
dc.date.issued2017-06
dc.description.abstractIn this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator ${}^C\!\Delta_+^{(\alpha,\beta,\gamma)}:= {}^C\!D_{x_0^+}^{1+\alpha} +{}^C\!D_{y_0^+}^{1+\beta} +{}^C\!D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$ and the fractional derivatives ${}^C\!D_{x_0^+}^{1+\alpha}$, ${}^C\!D_{y_0^+}^{1+\beta}$, ${}^C\!D_{z_0^+}^{1+\gamma}$ are in the Caputo sense. Applying integral transform methods we describe a complete family of eigenfunctions and fundamental solutions of the operator ${}^C\!\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. The solutions are expressed using the Mittag-Leffler function. From the family of fundamental solutions obtained we deduce a family of fundamental solutions of the corresponding fractional Dirac operator, which factorizes the fractional Laplace operator introduced in this paper.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationM. Ferreira & N. Vieira (2017) Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives, Complex Variables and Elliptic Equations, 62:9, 1237-1253, DOI: 10.1080/17476933.2016.1250401pt_PT
dc.identifier.doi10.1080/17476933.2016.1250401pt_PT
dc.identifier.issn1747-6933
dc.identifier.other1747-6941
dc.identifier.urihttp://hdl.handle.net/10400.8/3811
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherTaylor & Francispt_PT
dc.relation.publisherversionhttps://www.tandfonline.com/doi/full/10.1080/17476933.2016.1250401pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectFractional partial differential equationspt_PT
dc.subjectFractional Laplace and Dirac operatorspt_PT
dc.subjectCaputo derivativept_PT
dc.subjectEigenfunctionspt_PT
dc.subjectFundamental solutionpt_PT
dc.titleEigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivativespt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F04106%2F2013/PT
oaire.citation.endPage1253pt_PT
oaire.citation.issue9pt_PT
oaire.citation.startPage1237pt_PT
oaire.citation.titleComplex Variables and Elliptic Equationspt_PT
oaire.citation.volume62pt_PT
oaire.fundingStream5876
person.familyNameFerreira
person.familyNameVieira
person.givenNameMilton
person.givenNameNelson
person.identifier.ciencia-idCA19-2009-F26D
person.identifier.ciencia-id9418-DDFB-DE9D
person.identifier.orcid0000-0003-1816-8293
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-id55576073000
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublicationb1460cdc-4ced-46c6-a637-68b425d104dc
relation.isAuthorOfPublicationf530f82c-8351-4c64-a33e-4c34fe4ac22a
relation.isAuthorOfPublication.latestForDiscoveryf530f82c-8351-4c64-a33e-4c34fe4ac22a
relation.isProjectOfPublicationd62eccf5-8596-4ba5-afab-f0f258cfd08e
relation.isProjectOfPublication.latestForDiscoveryd62eccf5-8596-4ba5-afab-f0f258cfd08e

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