Publication
A higher dimensional fractional BorelāPompeiu formula and a related hypercomplex fractional operator calculus
dc.contributor.author | Ferreira, M. | |
dc.contributor.author | KrauĆhar, R. S. | |
dc.contributor.author | Rodrigues, M. M. | |
dc.contributor.author | Vieira, N. | |
dc.date.accessioned | 2021-03-19T11:38:40Z | |
dc.date.available | 2021-03-19T11:38:40Z | |
dc.date.issued | 2019-02-24 | |
dc.description | Acknowledgements: 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 FCTāFundação 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 (āPrograma de AĀøcĖoes Integradas Luso-AlemĖas/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.abstract | In 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.version | info:eu-repo/semantics/publishedVersion | pt_PT |
dc.identifier.citation | Ferreira, M, Krauβhar, RS, Rodrigues, MM, Vieira, N. A higher dimensional fractional BorelāPompeiu formula and a related hypercomplex fractional operator calculus. Math Meth Appl Sci. 2019; 42(10): 3633ā 3653. https://doi.org/10.1002/mma.5602 | pt_PT |
dc.identifier.doi | https://doi.org/10.1002/mma.5602 | pt_PT |
dc.identifier.issn | 1099-1476 | |
dc.identifier.issn | 0170-4214 | |
dc.identifier.uri | http://hdl.handle.net/10400.8/5525 | |
dc.language.iso | eng | pt_PT |
dc.peerreviewed | yes | pt_PT |
dc.publisher | Wiley Online Library | pt_PT |
dc.relation | Center for Research and Development in Mathematics and Applications | |
dc.relation.publisherversion | https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5602 | pt_PT |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
dc.subject | Fractional Clifford analysis | pt_PT |
dc.subject | Fractional derivatives | pt_PT |
dc.subject | Stokes's formula | pt_PT |
dc.subject | Borel-Pompeiu formula | pt_PT |
dc.subject | Cauchy's integral formula | pt_PT |
dc.subject | Hodge-type decomposition | pt_PT |
dc.title | A higher dimensional fractional BorelāPompeiu formula and a related hypercomplex fractional operator calculus | pt_PT |
dc.type | journal article | |
dspace.entity.type | Publication | |
oaire.awardTitle | Center for Research and Development in Mathematics and Applications | |
oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F04106%2F2019/PT | |
oaire.awardURI | info:eu-repo/grantAgreement/FCT/Investigador FCT/IF%2F00271%2F2014%2FCP1222%2FCT0008/PT | |
oaire.citation.endPage | 3653 | pt_PT |
oaire.citation.issue | 10 | pt_PT |
oaire.citation.startPage | 3633 | pt_PT |
oaire.citation.title | Mathematical Methods in the Applied Sciences | pt_PT |
oaire.citation.volume | 42 | pt_PT |
oaire.fundingStream | 6817 - DCRRNI ID | |
oaire.fundingStream | Investigador FCT | |
person.familyName | Ferreira | |
person.familyName | Rodrigues | |
person.familyName | Vieira | |
person.givenName | Milton | |
person.givenName | M. Manuela | |
person.givenName | Nelson | |
person.identifier.ciencia-id | CA19-2009-F26D | |
person.identifier.ciencia-id | 461D-A5E2-23BE | |
person.identifier.ciencia-id | 9418-DDFB-DE9D | |
person.identifier.orcid | 0000-0003-1816-8293 | |
person.identifier.orcid | 0000-0002-8834-5841 | |
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 | 22835991500 | |
person.identifier.scopus-author-id | 55576073000 | |
project.funder.identifier | http://doi.org/10.13039/501100001871 | |
project.funder.identifier | http://doi.org/10.13039/501100001871 | |
project.funder.name | Fundação para a Ciência e a Tecnologia | |
project.funder.name | Fundação para a Ciência e a Tecnologia | |
rcaap.rights | openAccess | pt_PT |
rcaap.type | article | pt_PT |
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relation.isProjectOfPublication.latestForDiscovery | 42ba4b66-8473-451e-88db-8598484579a8 |
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