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

Detalhes bibliográficos
Autor(a) principal: Ferreira, M.
Data de Publicação: 2018
Outros Autores: Rodrigues, M. M., Vieira, N.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.8/5526
Resumo: The 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.
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spelling A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator CalculusFractional Clifford analysisFractional derivativesTime-fractional parabolic Dirac operatorFundamental solutionBorel-Pompeiu formulaThe 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.Acknowledgment: 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).In 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.UID/MAT/04106/2019. A-15/17 / DAAD-PPP IF/00271/2014Springer NatureIC-OnlineFerreira, M.Rodrigues, M. M.Vieira, N.2021-03-19T12:09:08Z2018-12-242018-12-24T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/5526engFerreira, 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/s11785-018-00887-71661-826210.1007/s11785-018-00887-7info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-17T15:51:19Zoai:iconline.ipleiria.pt:10400.8/5526Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:49:01.282650Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus
title A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus
spellingShingle A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus
Ferreira, M.
Fractional Clifford analysis
Fractional derivatives
Time-fractional parabolic Dirac operator
Fundamental solution
Borel-Pompeiu formula
title_short A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus
title_full A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus
title_fullStr A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus
title_full_unstemmed A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus
title_sort A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus
author Ferreira, M.
author_facet Ferreira, M.
Rodrigues, M. M.
Vieira, N.
author_role author
author2 Rodrigues, M. M.
Vieira, N.
author2_role author
author
dc.contributor.none.fl_str_mv IC-Online
dc.contributor.author.fl_str_mv Ferreira, M.
Rodrigues, M. M.
Vieira, N.
dc.subject.por.fl_str_mv Fractional Clifford analysis
Fractional derivatives
Time-fractional parabolic Dirac operator
Fundamental solution
Borel-Pompeiu formula
topic Fractional Clifford analysis
Fractional derivatives
Time-fractional parabolic Dirac operator
Fundamental solution
Borel-Pompeiu formula
description The 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.
publishDate 2018
dc.date.none.fl_str_mv 2018-12-24
2018-12-24T00:00:00Z
2021-03-19T12:09:08Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.8/5526
url http://hdl.handle.net/10400.8/5526
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Ferreira, 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/s11785-018-00887-7
1661-8262
10.1007/s11785-018-00887-7
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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