Fractional derivatives: probability interpretation and frequency response of rational approximations
Main Author: | |
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Publication Date: | 2009 |
Format: | Article |
Language: | eng |
Source: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Download full: | http://hdl.handle.net/10400.22/4313 |
Summary: | The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts. |
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Fractional derivatives: probability interpretation and frequency response of rational approximationsFractional derivativeFractional calculusProbabilistic interpretationFrequency responseFraction approximationsThe theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.ElsevierRepositório Científico do Instituto Politécnico do PortoMachado, J. A. Tenreiro2014-04-04T11:31:29Z20092009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/4313eng1007-570410.1016/j.cnsns.2009.02.004info: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:RCAAP2023-03-13T12:44:26Zoai:recipp.ipp.pt:10400.22/4313Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:25:12.653160Repositório 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 derivatives: probability interpretation and frequency response of rational approximations |
title |
Fractional derivatives: probability interpretation and frequency response of rational approximations |
spellingShingle |
Fractional derivatives: probability interpretation and frequency response of rational approximations Machado, J. A. Tenreiro Fractional derivative Fractional calculus Probabilistic interpretation Frequency response Fraction approximations |
title_short |
Fractional derivatives: probability interpretation and frequency response of rational approximations |
title_full |
Fractional derivatives: probability interpretation and frequency response of rational approximations |
title_fullStr |
Fractional derivatives: probability interpretation and frequency response of rational approximations |
title_full_unstemmed |
Fractional derivatives: probability interpretation and frequency response of rational approximations |
title_sort |
Fractional derivatives: probability interpretation and frequency response of rational approximations |
author |
Machado, J. A. Tenreiro |
author_facet |
Machado, J. A. Tenreiro |
author_role |
author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
Machado, J. A. Tenreiro |
dc.subject.por.fl_str_mv |
Fractional derivative Fractional calculus Probabilistic interpretation Frequency response Fraction approximations |
topic |
Fractional derivative Fractional calculus Probabilistic interpretation Frequency response Fraction approximations |
description |
The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009 2009-01-01T00:00:00Z 2014-04-04T11:31:29Z |
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/10400.22/4313 |
url |
http://hdl.handle.net/10400.22/4313 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1007-5704 10.1016/j.cnsns.2009.02.004 |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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1799131345625022464 |