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A higher dimensional fractional Borel‐Pompeiu formula and a related hypercomplex fractional operator calculus

dc.contributor.authorFerreira, M.
dc.contributor.authorKraußhar, R. S.
dc.contributor.authorRodrigues, M. M.
dc.contributor.authorVieira, N.
dc.date.accessioned2021-03-19T11:38:40Z
dc.date.available2021-03-19T11:38:40Z
dc.date.issued2019-02-24
dc.descriptionAcknowledgements: The work of M. Ferreira, M.M. Rodrigues and N. Vieira was supported by Portuguese funds through CIDMACenter for Research and Development in Mathematics and Applications, and FCT–Fundação para a CiĆŖncia e a Tecnologia, within project UID/MAT/04106/2019. The work of the authors was supported by the project New Function Theoretic Methods in Computational Electrodynamics / Neue funktionentheoretische Methoden fĀØur instationĀØare PDE, funded by Programme for Cooperation in Science between Portugal and Germany (ā€œPrograma de AĀøc˜oes Integradas Luso-Alem˜as/2017ā€ - Acção No. A-19/08 - DAAD-PPP Deutschland-Portugal, Ref: 57340281). N. Vieira was also supported by FCT via the FCT Researcher Program 2014 (Ref: IF/00271/2014).
dc.description.abstractIn this paper, we develop a fractional integro-differential operator calculus for Clifford-algebra valued functions. To do that we introduce fractional analogs of the Teodorescu and Cauchy-Bitsadze operators and we investigate some of their mapping properties. As a main result, we prove a fractional Borel-Pompeiu formula based on a fractional Stokes formula. This tool in hand allows us to present a Hodge-type decomposition for the fractional Dirac operator. Our results exhibit an amazing duality relation between left and right operators and between Caputo and Riemann-Liouville fractional derivatives. We round off this paper by presenting a direct application to the resolution of boundary value problems related to Laplace operators of fractional order.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationFerreira, M, Krauβhar, RS, Rodrigues, MM, Vieira, N. A higher dimensional fractional Borel‐Pompeiu formula and a related hypercomplex fractional operator calculus. Math Meth Appl Sci. 2019; 42(10): 3633– 3653. https://doi.org/10.1002/mma.5602pt_PT
dc.identifier.doihttps://doi.org/10.1002/mma.5602pt_PT
dc.identifier.issn1099-1476
dc.identifier.issn0170-4214
dc.identifier.urihttp://hdl.handle.net/10400.8/5525
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherWiley Online Librarypt_PT
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relation.publisherversionhttps://onlinelibrary.wiley.com/doi/full/10.1002/mma.5602pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectFractional Clifford analysispt_PT
dc.subjectFractional derivativespt_PT
dc.subjectStokes's formulapt_PT
dc.subjectBorel-Pompeiu formulapt_PT
dc.subjectCauchy's integral formulapt_PT
dc.subjectHodge-type decompositionpt_PT
dc.titleA higher dimensional fractional Borel‐Pompeiu formula and a related hypercomplex fractional operator calculuspt_PT
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.awardURIinfo:eu-repo/grantAgreement/FCT/Investigador FCT/IF%2F00271%2F2014%2FCP1222%2FCT0008/PT
oaire.citation.endPage3653pt_PT
oaire.citation.issue10pt_PT
oaire.citation.startPage3633pt_PT
oaire.citation.titleMathematical Methods in the Applied Sciencespt_PT
oaire.citation.volume42pt_PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStreamInvestigador FCT
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.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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