Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives

Detalhes bibliográficos
Autor(a) principal: Antunes, Pedro R. S.
Data de Publicação: 2017
Outros Autores: Ferreira, Rui A. C.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/7177
Resumo: In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented-RBF method. Several examples illustrate the good performance of the numerical method.
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spelling Analysis of a class of boundary value problems depending on left and right Caputo fractional derivativesFractional calculusCaputo derivativeBoundary value problemRadial basis functionsIn this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented-RBF method. Several examples illustrate the good performance of the numerical method.P.A. is partially supported by FCT, Portugal, through the program “Investigador FCT” with reference IF/00177/2013 and the scientific projects PEstOE/MAT/UI0208/2013 and PTDC/MAT-CAL/4334/2014. R.F. was supported by the “Fundação para a Ciência e a Tecnologia (FCT)” through the program “Investigador FCT” with reference IF/01345/2014.ElsevierRepositório AbertoAntunes, Pedro R. S.Ferreira, Rui A. C.2018-07-01T00:30:14Z2017-072017-07-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/7177eng1007-5704https://doi.org/10.1016/j.cnsns.2017.01.017info: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:RCAAP2023-11-16T15:25:58Zoai:repositorioaberto.uab.pt:10400.2/7177Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:47:26.139216Repositório 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 Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
title Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
spellingShingle Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
Antunes, Pedro R. S.
Fractional calculus
Caputo derivative
Boundary value problem
Radial basis functions
title_short Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
title_full Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
title_fullStr Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
title_full_unstemmed Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
title_sort Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
author Antunes, Pedro R. S.
author_facet Antunes, Pedro R. S.
Ferreira, Rui A. C.
author_role author
author2 Ferreira, Rui A. C.
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Antunes, Pedro R. S.
Ferreira, Rui A. C.
dc.subject.por.fl_str_mv Fractional calculus
Caputo derivative
Boundary value problem
Radial basis functions
topic Fractional calculus
Caputo derivative
Boundary value problem
Radial basis functions
description In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented-RBF method. Several examples illustrate the good performance of the numerical method.
publishDate 2017
dc.date.none.fl_str_mv 2017-07
2017-07-01T00:00:00Z
2018-07-01T00:30:14Z
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/10400.2/7177
url http://hdl.handle.net/10400.2/7177
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1007-5704
https://doi.org/10.1016/j.cnsns.2017.01.017
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
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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