Publication
Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives
dc.contributor.author | Ferreira, Milton | |
dc.contributor.author | Vieira, Nelson Felipe Loureiro | |
dc.date.accessioned | 2019-02-07T14:25:01Z | |
dc.date.available | 2019-02-07T14:25:01Z | |
dc.date.issued | 2017-06 | |
dc.description.abstract | In 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.version | info:eu-repo/semantics/publishedVersion | pt_PT |
dc.identifier.citation | M. 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: 10.1080/17476933.2016.1250401 | pt_PT |
dc.identifier.doi | 10.1080/17476933.2016.1250401 | pt_PT |
dc.identifier.issn | 1747-6933 | |
dc.identifier.other | 1747-6941 | |
dc.identifier.uri | http://hdl.handle.net/10400.8/3811 | |
dc.language.iso | eng | pt_PT |
dc.peerreviewed | yes | pt_PT |
dc.publisher | Taylor & Francis | pt_PT |
dc.relation.publisherversion | https://www.tandfonline.com/doi/full/10.1080/17476933.2016.1250401 | pt_PT |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
dc.subject | Fractional partial differential equations | pt_PT |
dc.subject | Fractional Laplace and Dirac operators | pt_PT |
dc.subject | Caputo derivative | pt_PT |
dc.subject | Eigenfunctions | pt_PT |
dc.subject | Fundamental solution | pt_PT |
dc.title | Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives | pt_PT |
dc.type | journal article | |
dspace.entity.type | Publication | |
oaire.awardURI | info:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F04106%2F2013/PT | |
oaire.citation.endPage | 1253 | pt_PT |
oaire.citation.issue | 9 | pt_PT |
oaire.citation.startPage | 1237 | pt_PT |
oaire.citation.title | Complex Variables and Elliptic Equations | pt_PT |
oaire.citation.volume | 62 | pt_PT |
oaire.fundingStream | 5876 | |
person.familyName | Ferreira | |
person.familyName | Vieira | |
person.givenName | Milton | |
person.givenName | Nelson | |
person.identifier.ciencia-id | CA19-2009-F26D | |
person.identifier.ciencia-id | 9418-DDFB-DE9D | |
person.identifier.orcid | 0000-0003-1816-8293 | |
person.identifier.orcid | 0000-0001-8756-4893 | |
person.identifier.rid | A-2004-2015 | |
person.identifier.rid | H-9130-2013 | |
person.identifier.scopus-author-id | 12144179800 | |
person.identifier.scopus-author-id | 55576073000 | |
project.funder.identifier | http://doi.org/10.13039/501100001871 | |
project.funder.name | Fundação para a Ciência e a Tecnologia | |
rcaap.rights | openAccess | pt_PT |
rcaap.type | article | pt_PT |
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