Fractional Scale Calculus

Detalhes bibliográficos
Autor(a) principal: Ortigueira, Manuel D.
Data de Publicação: 2023
Outros Autores: Bohannan, Gary W.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/158090
Resumo: Funding Information: The first author was partially funded by National Funds through the Foundation for Science and Technology of Portugal, under the projects UIDB/00066/2020. Publisher Copyright: © 2023 by the authors.
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spelling Fractional Scale CalculusHadamard vs. LiouvilleHadamard derivativeLiouville derivativelogarithmic seriesscale derivativetempered derivativeAnalysisStatistical and Nonlinear PhysicsStatistics and ProbabilityFunding Information: The first author was partially funded by National Funds through the Foundation for Science and Technology of Portugal, under the projects UIDB/00066/2020. Publisher Copyright: © 2023 by the authors.A general fractional scale derivative is introduced and studied. Its relation with the Hadamard derivatives is established and reformulated. A new derivative similar to the Grünwald–Letnikov’s is deduced. Tempered versions are also introduced. Scale-invariant systems are described and exemplified. For solving the corresponding differential equations, a new logarithmic Mittag-Leffler series is proposed.CTS - Centro de Tecnologia e SistemasUNINOVA-Instituto de Desenvolvimento de Novas TecnologiasDEE - Departamento de Engenharia Electrotécnica e de ComputadoresRUNOrtigueira, Manuel D.Bohannan, Gary W.2023-09-21T22:14:56Z2023-042023-04-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article19application/pdfhttp://hdl.handle.net/10362/158090eng2504-3110PURE: 72085745https://doi.org/10.3390/fractalfract7040296info: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:RCAAP2024-03-11T05:40:22Zoai:run.unl.pt:10362/158090Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:56:58.730912Repositório 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 Fractional Scale Calculus
Hadamard vs. Liouville
title Fractional Scale Calculus
spellingShingle Fractional Scale Calculus
Ortigueira, Manuel D.
Hadamard derivative
Liouville derivative
logarithmic series
scale derivative
tempered derivative
Analysis
Statistical and Nonlinear Physics
Statistics and Probability
title_short Fractional Scale Calculus
title_full Fractional Scale Calculus
title_fullStr Fractional Scale Calculus
title_full_unstemmed Fractional Scale Calculus
title_sort Fractional Scale Calculus
author Ortigueira, Manuel D.
author_facet Ortigueira, Manuel D.
Bohannan, Gary W.
author_role author
author2 Bohannan, Gary W.
author2_role author
dc.contributor.none.fl_str_mv CTS - Centro de Tecnologia e Sistemas
UNINOVA-Instituto de Desenvolvimento de Novas Tecnologias
DEE - Departamento de Engenharia Electrotécnica e de Computadores
RUN
dc.contributor.author.fl_str_mv Ortigueira, Manuel D.
Bohannan, Gary W.
dc.subject.por.fl_str_mv Hadamard derivative
Liouville derivative
logarithmic series
scale derivative
tempered derivative
Analysis
Statistical and Nonlinear Physics
Statistics and Probability
topic Hadamard derivative
Liouville derivative
logarithmic series
scale derivative
tempered derivative
Analysis
Statistical and Nonlinear Physics
Statistics and Probability
description Funding Information: The first author was partially funded by National Funds through the Foundation for Science and Technology of Portugal, under the projects UIDB/00066/2020. Publisher Copyright: © 2023 by the authors.
publishDate 2023
dc.date.none.fl_str_mv 2023-09-21T22:14:56Z
2023-04
2023-04-01T00:00:00Z
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/10362/158090
url http://hdl.handle.net/10362/158090
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2504-3110
PURE: 72085745
https://doi.org/10.3390/fractalfract7040296
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 19
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
instacron_str RCAAP
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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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