Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels

Detalhes bibliográficos
Autor(a) principal: Cruz, Fátima
Data de Publicação: 2021
Outros Autores: Almeida, Ricardo, Martins, Natália
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/30985
Resumo: In this work we study necessary and sufficient optimality conditions for variational problems dealing with a new fractional derivative. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with arbitrary kernels. After proving a fractional integration by parts formula, we obtain the Euler–Lagrange equation and natural boundary conditions for the fundamental variational problem. Also, fractional variational problems with integral and holonomic constraints are considered. We end with some examples to exemplify our results.
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spelling Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernelsFractional calculusCalculus of variationsEuler-Lagrange equationIsoperimetric problemsHolonomic problemsIn this work we study necessary and sufficient optimality conditions for variational problems dealing with a new fractional derivative. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with arbitrary kernels. After proving a fractional integration by parts formula, we obtain the Euler–Lagrange equation and natural boundary conditions for the fundamental variational problem. Also, fractional variational problems with integral and holonomic constraints are considered. We end with some examples to exemplify our results.AIMS Press2021-03-23T09:33:50Z2021-01-01T00:00:00Z2021info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/30985eng10.3934/math.2021315Cruz, FátimaAlmeida, RicardoMartins, Natáliainfo: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:RCAAP2024-02-22T11:59:48Zoai:ria.ua.pt:10773/30985Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:02:57.136585Repositório 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 Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels
title Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels
spellingShingle Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels
Cruz, Fátima
Fractional calculus
Calculus of variations
Euler-Lagrange equation
Isoperimetric problems
Holonomic problems
title_short Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels
title_full Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels
title_fullStr Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels
title_full_unstemmed Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels
title_sort Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels
author Cruz, Fátima
author_facet Cruz, Fátima
Almeida, Ricardo
Martins, Natália
author_role author
author2 Almeida, Ricardo
Martins, Natália
author2_role author
author
dc.contributor.author.fl_str_mv Cruz, Fátima
Almeida, Ricardo
Martins, Natália
dc.subject.por.fl_str_mv Fractional calculus
Calculus of variations
Euler-Lagrange equation
Isoperimetric problems
Holonomic problems
topic Fractional calculus
Calculus of variations
Euler-Lagrange equation
Isoperimetric problems
Holonomic problems
description In this work we study necessary and sufficient optimality conditions for variational problems dealing with a new fractional derivative. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with arbitrary kernels. After proving a fractional integration by parts formula, we obtain the Euler–Lagrange equation and natural boundary conditions for the fundamental variational problem. Also, fractional variational problems with integral and holonomic constraints are considered. We end with some examples to exemplify our results.
publishDate 2021
dc.date.none.fl_str_mv 2021-03-23T09:33:50Z
2021-01-01T00:00:00Z
2021
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/10773/30985
url http://hdl.handle.net/10773/30985
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.3934/math.2021315
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 AIMS Press
publisher.none.fl_str_mv AIMS Press
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
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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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