What is a fractional derivative?

Detalhes bibliográficos
Autor(a) principal: Ortigueira, Manuel
Data de Publicação: 2015
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/10400.22/6952
Resumo: This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald–Letnikov, Riemann–Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.
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spelling What is a fractional derivative?Fractional derivativeRiesz potentialFractional calculusThis paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald–Letnikov, Riemann–Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.ElsevierRepositório Científico do Instituto Politécnico do PortoOrtigueira, ManuelMachado, J. A. Tenreiro2015-11-19T16:57:15Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/6952eng10.1016/j.jcp.2014.07.019metadata only accessinfo: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:RCAAP2023-03-13T12:47:16Zoai:recipp.ipp.pt:10400.22/6952Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:27:22.924667Repositório 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 What is a fractional derivative?
title What is a fractional derivative?
spellingShingle What is a fractional derivative?
Ortigueira, Manuel
Fractional derivative
Riesz potential
Fractional calculus
title_short What is a fractional derivative?
title_full What is a fractional derivative?
title_fullStr What is a fractional derivative?
title_full_unstemmed What is a fractional derivative?
title_sort What is a fractional derivative?
author Ortigueira, Manuel
author_facet Ortigueira, Manuel
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
Machado, J. A. Tenreiro
dc.subject.por.fl_str_mv Fractional derivative
Riesz potential
Fractional calculus
topic Fractional derivative
Riesz potential
Fractional calculus
description This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald–Letnikov, Riemann–Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.
publishDate 2015
dc.date.none.fl_str_mv 2015-11-19T16:57:15Z
2015
2015-01-01T00:00:00Z
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/10400.22/6952
url http://hdl.handle.net/10400.22/6952
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1016/j.jcp.2014.07.019
dc.rights.driver.fl_str_mv metadata only access
info:eu-repo/semantics/openAccess
rights_invalid_str_mv metadata only access
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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