An expansion formula with higher-order derivatives for fractional operators of variable order

Detalhes bibliográficos
Autor(a) principal: Almeida, R.
Data de Publicação: 2013
Outros Autores: Torres, D.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/10773/11891
Resumo: We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type.
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spelling An expansion formula with higher-order derivatives for fractional operators of variable orderAnalytical errorMarchaud fractional orderMathematical analysisMathematical parametersRiemann-Liouville fractional orderWe obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type.Hindawi2014-02-25T18:35:43Z2013-01-01T00:00:00Z2013info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/11891eng1537-744X10.1155/2013/915437Almeida, R.Torres, D.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:RCAAP2024-02-22T11:21:09Zoai:ria.ua.pt:10773/11891Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:48:03.987584Repositório 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 An expansion formula with higher-order derivatives for fractional operators of variable order
title An expansion formula with higher-order derivatives for fractional operators of variable order
spellingShingle An expansion formula with higher-order derivatives for fractional operators of variable order
Almeida, R.
Analytical error
Marchaud fractional order
Mathematical analysis
Mathematical parameters
Riemann-Liouville fractional order
title_short An expansion formula with higher-order derivatives for fractional operators of variable order
title_full An expansion formula with higher-order derivatives for fractional operators of variable order
title_fullStr An expansion formula with higher-order derivatives for fractional operators of variable order
title_full_unstemmed An expansion formula with higher-order derivatives for fractional operators of variable order
title_sort An expansion formula with higher-order derivatives for fractional operators of variable order
author Almeida, R.
author_facet Almeida, R.
Torres, D.F.M.
author_role author
author2 Torres, D.F.M.
author2_role author
dc.contributor.author.fl_str_mv Almeida, R.
Torres, D.F.M.
dc.subject.por.fl_str_mv Analytical error
Marchaud fractional order
Mathematical analysis
Mathematical parameters
Riemann-Liouville fractional order
topic Analytical error
Marchaud fractional order
Mathematical analysis
Mathematical parameters
Riemann-Liouville fractional order
description We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type.
publishDate 2013
dc.date.none.fl_str_mv 2013-01-01T00:00:00Z
2013
2014-02-25T18:35:43Z
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/10773/11891
url http://hdl.handle.net/10773/11891
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1537-744X
10.1155/2013/915437
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 Hindawi
publisher.none.fl_str_mv Hindawi
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
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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