Caputo derivatives of fractional variable order: numerical approximations

Detalhes bibliográficos
Autor(a) principal: Tavares, Dina
Data de Publicação: 2016
Outros Autores: Almeida, Ricardo, Torres, Delfim F. 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/10773/15022
Resumo: We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is obtained in terms of standard (integerorder) derivatives only. Estimations for the error of the approximations are also provided. We then compare the numerical approximation of some test function with its exact fractional derivative. We end with an exemplification of how the presented methods can be used to solve partial fractional differential equations of variable order.
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spelling Caputo derivatives of fractional variable order: numerical approximationsFractional calculusFractional variable orderFractional differential equationsApproximation methodsWe present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is obtained in terms of standard (integerorder) derivatives only. Estimations for the error of the approximations are also provided. We then compare the numerical approximation of some test function with its exact fractional derivative. We end with an exemplification of how the presented methods can be used to solve partial fractional differential equations of variable order.Elsevier2018-07-20T14:00:51Z2016-06-01T00:00:00Z2016-062017-06-01T09:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15022eng1007-570410.1016/j.cnsns.2015.10.027Tavares, DinaAlmeida, RicardoTorres, Delfim F. M.info: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:RCAAP2024-02-22T11:27:47Zoai:ria.ua.pt:10773/15022Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:30.204638Repositório 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 Caputo derivatives of fractional variable order: numerical approximations
title Caputo derivatives of fractional variable order: numerical approximations
spellingShingle Caputo derivatives of fractional variable order: numerical approximations
Tavares, Dina
Fractional calculus
Fractional variable order
Fractional differential equations
Approximation methods
title_short Caputo derivatives of fractional variable order: numerical approximations
title_full Caputo derivatives of fractional variable order: numerical approximations
title_fullStr Caputo derivatives of fractional variable order: numerical approximations
title_full_unstemmed Caputo derivatives of fractional variable order: numerical approximations
title_sort Caputo derivatives of fractional variable order: numerical approximations
author Tavares, Dina
author_facet Tavares, Dina
Almeida, Ricardo
Torres, Delfim F. M.
author_role author
author2 Almeida, Ricardo
Torres, Delfim F. M.
author2_role author
author
dc.contributor.author.fl_str_mv Tavares, Dina
Almeida, Ricardo
Torres, Delfim F. M.
dc.subject.por.fl_str_mv Fractional calculus
Fractional variable order
Fractional differential equations
Approximation methods
topic Fractional calculus
Fractional variable order
Fractional differential equations
Approximation methods
description We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is obtained in terms of standard (integerorder) derivatives only. Estimations for the error of the approximations are also provided. We then compare the numerical approximation of some test function with its exact fractional derivative. We end with an exemplification of how the presented methods can be used to solve partial fractional differential equations of variable order.
publishDate 2016
dc.date.none.fl_str_mv 2016-06-01T00:00:00Z
2016-06
2017-06-01T09:00:00Z
2018-07-20T14:00:51Z
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/10773/15022
url http://hdl.handle.net/10773/15022
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1007-5704
10.1016/j.cnsns.2015.10.027
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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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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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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