Repository logo
 
Publication

A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus

2018-12-24Journal article Open access
Simple item page
dc.contributor.authorFerreira, M.
dc.contributor.authorRodrigues, M. M.
dc.contributor.authorVieira, N.
dc.date.accessioned2021-03-19T12:09:08Z
dc.date.available2021-03-19T12:09:08Z
dc.date.issued2018-12-24
dc.descriptionThe final version is published in Complex Analysis and Operator Theory, 13-No.6, (2019). Received: 8 May 2018 / Accepted: 24 December 2018 / Published online: 11 January 2019.pt_PT
dc.descriptionAcknowledgment: The work of M. Ferreira, M.M. Rodrigues and N. Vieira was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Funda¸c˜ao para a Ciˆencia e a Tecnologia, within project UID/MAT/04106/2019. The work of the authors was supported by the project New Function Theoretical Methods in Computational Electrodynamics / Neue funktionentheoretische Methoden f¨ur instation¨are PDE, funded by Programme for Cooperation in Science between Portugal and Germany (“Programa de A¸c˜oes Integradas Luso-Alem˜as 2017” - DAAD-CRUP - Ação No. A-15/17 / 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 time-fractional operator calculus in fractional Clifford analysis. Initially, we study the $L_p$-integrability of the fundamental solutions of the multi-dimensional time-fractional diffusion operator and the associated time-fractional parabolic Dirac operator. Then we introduce the time-fractional analogs of the Teodorescu and Cauchy-Bitsadze operators in a cylindrical domain, and we investigate their main mapping properties. As a main result, we prove a time-fractional version of the Borel-Pompeiu formula based on a time-fractional Stokes' formula. This tool in hand allows us to present a Hodge-type decomposition for the forward time-fractional parabolic Dirac operator with left Caputo fractional derivative in the time coordinate. The obtained results exhibit an interesting duality relation between forward and backward parabolic Dirac operators and Caputo and Riemann-Liouville time-fractional derivatives. We round off this paper by giving a direct application of the obtained results for solving time-fractional boundary value problems.pt_PT
dc.description.abstractUID/MAT/04106/2019. A-15/17 / DAAD-PPP IF/00271/2014pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationFerreira, M., Rodrigues, M.M. & Vieira, N. A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus. Complex Anal. Oper. Theory 13, 2495–2526 (2019). https://doi.org/10.1007/s11785-018-00887-7pt_PT
dc.identifier.doi10.1007/s11785-018-00887-7pt_PT
dc.identifier.issn1661-8262
dc.identifier.issn1661-8254
dc.identifier.urihttp://hdl.handle.net/10400.8/5526
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringer Naturept_PT
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relation.publisherversionhttps://link.springer.com/article/10.1007/s11785-018-00887-7pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectFractional Clifford analysispt_PT
dc.subjectFractional derivativespt_PT
dc.subjectTime-fractional parabolic Dirac operatorpt_PT
dc.subjectFundamental solutionpt_PT
dc.subjectBorel-Pompeiu formulapt_PT
dc.titleA Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex 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.endPage2526pt_PT
oaire.citation.issue6pt_PT
oaire.citation.startPage2495pt_PT
oaire.citation.titleComplex Analysis and Operator Theorypt_PT
oaire.citation.volume13pt_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
relation.isAuthorOfPublicationb1460cdc-4ced-46c6-a637-68b425d104dc
relation.isAuthorOfPublication57767487-249d-4111-a6c5-a22fed15d8ea
relation.isAuthorOfPublicationf530f82c-8351-4c64-a33e-4c34fe4ac22a
relation.isAuthorOfPublication.latestForDiscovery57767487-249d-4111-a6c5-a22fed15d8ea
relation.isProjectOfPublication42ba4b66-8473-451e-88db-8598484579a8
relation.isProjectOfPublicatione69c6f10-ba1b-4f3d-a441-2a7d31c12b2c
relation.isProjectOfPublication.latestForDiscovery42ba4b66-8473-451e-88db-8598484579a8

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Time_fract_Borel_Pompeiu_formula_Post_Print.pdf
Size:
541.97 KB
Format:
Adobe Portable Document Format
Description:
Download

Collections

ESTG - Artigos em revistas internacionais