New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter

Detalhes bibliográficos
Autor(a) principal: Almeida, Ricardo
Data de Publicação: 2021
Outros Autores: 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/10773/31119
Resumo: This work presents optimality conditions for several fractional variational problems where the Lagrange function depends on fractional order operators, the initial and final state values, and a free parameter. The fractional derivatives considered in this paper are the Riemann–Liouville and the Caputo derivatives with respect to an arbitrary kernel. The new variational problems studied here are generalizations of several types of variational problems, and therefore, our results generalize well-known results from the fractional calculus of variations. Namely, we prove conditions useful to determine the optimal orders of the fractional derivatives and necessary optimality conditions involving time delays and arbitrary real positive fractional orders. Sufficient conditions for such problems are also studied. Illustrative examples are provided.
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spelling New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameterFractional calculusEuler–Lagrange equationNatural boundary conditionsTime delayThis work presents optimality conditions for several fractional variational problems where the Lagrange function depends on fractional order operators, the initial and final state values, and a free parameter. The fractional derivatives considered in this paper are the Riemann–Liouville and the Caputo derivatives with respect to an arbitrary kernel. The new variational problems studied here are generalizations of several types of variational problems, and therefore, our results generalize well-known results from the fractional calculus of variations. Namely, we prove conditions useful to determine the optimal orders of the fractional derivatives and necessary optimality conditions involving time delays and arbitrary real positive fractional orders. Sufficient conditions for such problems are also studied. Illustrative examples are provided.MDPI2021-04-06T18:34:30Z2021-01-01T00:00:00Z2021info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/31119eng10.3390/sym13040592Almeida, 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:RCAAP2024-02-22T12:00:05Zoai:ria.ua.pt:10773/31119Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:03:04.687934Repositório 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 New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter
title New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter
spellingShingle New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter
Almeida, Ricardo
Fractional calculus
Euler–Lagrange equation
Natural boundary conditions
Time delay
title_short New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter
title_full New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter
title_fullStr New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter
title_full_unstemmed New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter
title_sort New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter
author Almeida, Ricardo
author_facet Almeida, Ricardo
Martins, Natália
author_role author
author2 Martins, Natália
author2_role author
dc.contributor.author.fl_str_mv Almeida, Ricardo
Martins, Natália
dc.subject.por.fl_str_mv Fractional calculus
Euler–Lagrange equation
Natural boundary conditions
Time delay
topic Fractional calculus
Euler–Lagrange equation
Natural boundary conditions
Time delay
description This work presents optimality conditions for several fractional variational problems where the Lagrange function depends on fractional order operators, the initial and final state values, and a free parameter. The fractional derivatives considered in this paper are the Riemann–Liouville and the Caputo derivatives with respect to an arbitrary kernel. The new variational problems studied here are generalizations of several types of variational problems, and therefore, our results generalize well-known results from the fractional calculus of variations. Namely, we prove conditions useful to determine the optimal orders of the fractional derivatives and necessary optimality conditions involving time delays and arbitrary real positive fractional orders. Sufficient conditions for such problems are also studied. Illustrative examples are provided.
publishDate 2021
dc.date.none.fl_str_mv 2021-04-06T18:34:30Z
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/10773/31119
url http://hdl.handle.net/10773/31119
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.3390/sym13040592
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
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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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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