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Fundamental Solution for Natural Powers of the Fractional Laplace and Dirac Operators in the Riemann–Liouville Sense

2019-11-10Journal article Open access
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datacite.subject.fosCiências Naturais::Matemáticas
dc.contributor.authorTeodoro, A. Di
dc.contributor.authorFerreira, M.
dc.contributor.authorVieira, N.
dc.date.accessioned2025-10-06T15:02:13Z
dc.date.available2025-10-06T15:02:13Z
dc.date.issued2019-11-10
dc.description.abstractIn this paper, we study the fundamental solution of natural powers of the n-parameter fractional Laplace and Dirac operators defined via Riemann–Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation starting from the fundamental solutions of the fractional Laplace Δa+α and Dirac Da+α operators, admitting a summable fractional derivative. The family of fundamental solutions of the corresponding natural powers of fractional Laplace and Dirac operators are expressed in operator form using the Mittag–Leffler function.eng
dc.description.sponsorshipA. Di Teodoro was supported by Colegio de Ciencias e Ingenierías de la Universidad San Francisco de Quito. The work of M. Ferreira and N. Vieira was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Fundação para a Ciência e a Tecnologia, within project UID/MAT/04106/2019. N. Vieira was also supported by FCT via the FCT Researcher Program 2014 (Ref: IF/00271/2014).
dc.identifier.citationTeodoro, A.D., Ferreira, M. & Vieira, N. Fundamental Solution for Natural Powers of the Fractional Laplace and Dirac Operators in the Riemann–Liouville Sense. Adv. Appl. Clifford Algebras 30, 3 (2020). https://doi.org/10.1007/s00006-019-1029-1.
dc.identifier.doi10.1007/s00006-019-1029-1
dc.identifier.issn0188-7009
dc.identifier.urihttp://hdl.handle.net/10400.8/14212
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer Nature
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relation.hasversionhttps://link.springer.com/article/10.1007/s00006-019-1029-1
dc.relation.ispartofAdvances in Applied Clifford Algebras
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectFractional Clifford analysis
dc.subjectFractional derivatives
dc.subjectFundamental solution
dc.subjectPoisson’s equation
dc.subjectLaplace transform
dc.titleFundamental Solution for Natural Powers of the Fractional Laplace and Dirac Operators in the Riemann–Liouville Senseeng
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/UID%2FMAT%2F04106%2F2019/PT
oaire.citation.endPage18
oaire.citation.startPage1
oaire.citation.titleAdvances in Applied Clifford Algebras
oaire.citation.volume30
oaire.fundingStream6817 - DCRRNI ID
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyNameFerreira
person.givenNameMilton
person.identifier.ciencia-idCA19-2009-F26D
person.identifier.orcid0000-0003-1816-8293
person.identifier.ridA-2004-2015
person.identifier.scopus-author-id12144179800
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
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relation.isAuthorOfPublication.latestForDiscoveryb1460cdc-4ced-46c6-a637-68b425d104dc
relation.isProjectOfPublication42ba4b66-8473-451e-88db-8598484579a8
relation.isProjectOfPublication.latestForDiscovery42ba4b66-8473-451e-88db-8598484579a8

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In this paper, we study the fundamental solution of natural powers of the n-parameter fractional Laplace and Dirac operators defined via Riemann–Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation starting from the fundamental solutions of the fractional Laplace Δa+α and Dirac Da+α operators, admitting a summable fractional derivative. The family of fundamental solutions of the corresponding natural powers of fractional Laplace and Dirac operators are expressed in operator form using the Mittag–Leffler function.
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