An expansion formula with higher-order derivatives for fractional operators of variable order
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | |
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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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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 |
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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 |
repository.mail.fl_str_mv |
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1799137532094447616 |