New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties

Detalhes bibliográficos
Autor(a) principal: Ortigueira, Manuel D.
Data de Publicação: 2020
Outros Autores: Machado, J. A. Tenreiro
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.22/19020
Resumo: In this paper we introduce new discrete-time derivative concepts based on the bilinear (Tustin) transformation. From the new formulation, we obtain derivatives that exhibit a high degree of similarity with the continuous-time Grünwald-Letnikov derivatives. Their properties are described highlighting one important feature, namely that such derivatives have always long memory.
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spelling New discrete-time fractional derivatives based on the bilinear transformation: Definitions and propertiesDiscrete-timeFractional derivativeTime scaleBilinear transformationIn this paper we introduce new discrete-time derivative concepts based on the bilinear (Tustin) transformation. From the new formulation, we obtain derivatives that exhibit a high degree of similarity with the continuous-time Grünwald-Letnikov derivatives. Their properties are described highlighting one important feature, namely that such derivatives have always long memory.This work was partially funded by National Funds through theFoundation for Science and Technology of Portugal, under the projects UIDB/00066/2020.ElsevierRepositório Científico do Instituto Politécnico do PortoOrtigueira, Manuel D.Machado, J. A. Tenreiro2021-12-07T15:22:38Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/19020eng10.1016/j.jare.2020.02.011info: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:RCAAP2023-03-13T13:12:46Zoai:recipp.ipp.pt:10400.22/19020Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:39:04.577637Repositório 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 New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
spellingShingle New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
Ortigueira, Manuel D.
Discrete-time
Fractional derivative
Time scale
Bilinear transformation
title_short New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title_full New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title_fullStr New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title_full_unstemmed New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title_sort New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
author Ortigueira, Manuel D.
author_facet Ortigueira, Manuel D.
Machado, J. A. Tenreiro
author_role author
author2 Machado, J. A. Tenreiro
author2_role author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico do Porto
dc.contributor.author.fl_str_mv Ortigueira, Manuel D.
Machado, J. A. Tenreiro
dc.subject.por.fl_str_mv Discrete-time
Fractional derivative
Time scale
Bilinear transformation
topic Discrete-time
Fractional derivative
Time scale
Bilinear transformation
description In this paper we introduce new discrete-time derivative concepts based on the bilinear (Tustin) transformation. From the new formulation, we obtain derivatives that exhibit a high degree of similarity with the continuous-time Grünwald-Letnikov derivatives. Their properties are described highlighting one important feature, namely that such derivatives have always long memory.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
2021-12-07T15:22:38Z
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/10400.22/19020
url http://hdl.handle.net/10400.22/19020
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1016/j.jare.2020.02.011
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 Elsevier
publisher.none.fl_str_mv Elsevier
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
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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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