How Many Fractional Derivatives Are There?

Detalhes bibliográficos
Autor(a) principal: Valério, Duarte
Data de Publicação: 2022
Outros Autores: Ortigueira, Manuel D., Lopes, António M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/143802
Resumo: Funding: This work was partially funded by National Funds through the FCT-Foundation for Science and Technology within the scope of the CTS Research Unit—Center of Technology and Systems/UNINOVA/FC /NOVA, under the reference UIDB/00066/2020, and also by FCT through IDMEC, under LAETA, project UID/EMS/50022/2020. Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
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spelling How Many Fractional Derivatives Are There?fractional calculusfractional derivativesignals and systemsMathematics(all)Funding: This work was partially funded by National Funds through the FCT-Foundation for Science and Technology within the scope of the CTS Research Unit—Center of Technology and Systems/UNINOVA/FC /NOVA, under the reference UIDB/00066/2020, and also by FCT through IDMEC, under LAETA, project UID/EMS/50022/2020. Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.In this paper, we introduce a unified fractional derivative, defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained. We study the one-sided derivatives and show that most known derivatives are particular cases. We consider also some myths of Fractional Calculus and false fractional derivatives. The results are expected to contribute to limit the appearance of derivatives that differ from existing ones just because they are defined on distinct domains, and to prevent the ambiguous use of the concept of fractional derivative.CTS - Centro de Tecnologia e SistemasDEE2010-B2 SistemasUNINOVA-Instituto de Desenvolvimento de Novas TecnologiasDEE - Departamento de Engenharia Electrotécnica e de ComputadoresRUNValério, DuarteOrtigueira, Manuel D.Lopes, António M.2022-09-16T22:28:29Z2022-02-252022-02-25T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article18application/pdfhttp://hdl.handle.net/10362/143802eng2227-7390PURE: 46582726https://doi.org/10.3390/math10050737info: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:RCAAP2024-03-11T05:22:33Zoai:run.unl.pt:10362/143802Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:51:09.168576Repositório 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 How Many Fractional Derivatives Are There?
title How Many Fractional Derivatives Are There?
spellingShingle How Many Fractional Derivatives Are There?
Valério, Duarte
fractional calculus
fractional derivative
signals and systems
Mathematics(all)
title_short How Many Fractional Derivatives Are There?
title_full How Many Fractional Derivatives Are There?
title_fullStr How Many Fractional Derivatives Are There?
title_full_unstemmed How Many Fractional Derivatives Are There?
title_sort How Many Fractional Derivatives Are There?
author Valério, Duarte
author_facet Valério, Duarte
Ortigueira, Manuel D.
Lopes, António M.
author_role author
author2 Ortigueira, Manuel D.
Lopes, António M.
author2_role author
author
dc.contributor.none.fl_str_mv CTS - Centro de Tecnologia e Sistemas
DEE2010-B2 Sistemas
UNINOVA-Instituto de Desenvolvimento de Novas Tecnologias
DEE - Departamento de Engenharia Electrotécnica e de Computadores
RUN
dc.contributor.author.fl_str_mv Valério, Duarte
Ortigueira, Manuel D.
Lopes, António M.
dc.subject.por.fl_str_mv fractional calculus
fractional derivative
signals and systems
Mathematics(all)
topic fractional calculus
fractional derivative
signals and systems
Mathematics(all)
description Funding: This work was partially funded by National Funds through the FCT-Foundation for Science and Technology within the scope of the CTS Research Unit—Center of Technology and Systems/UNINOVA/FC /NOVA, under the reference UIDB/00066/2020, and also by FCT through IDMEC, under LAETA, project UID/EMS/50022/2020. Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
publishDate 2022
dc.date.none.fl_str_mv 2022-09-16T22:28:29Z
2022-02-25
2022-02-25T00:00:00Z
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/10362/143802
url http://hdl.handle.net/10362/143802
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2227-7390
PURE: 46582726
https://doi.org/10.3390/math10050737
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 18
application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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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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