Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels
Autor(a) principal: | |
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Data de Publicação: | 2021 |
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/10773/30985 |
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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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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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 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 |
repository.mail.fl_str_mv |
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1799137684716781568 |