A generalization of a fractional variational problem with dependence on the boundaries 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/10773/30987
Resumo: In this paper, we present a new fractional variational problem where the Lagrangian depends not only on the independent variable, an unknown function and its left- and right-sided Caputo fractional derivatives with respect to another function, but also on the endpoint conditions and a free parameter. The main results of this paper are necessary and sufficient optimality conditions for variational problems with or without isoperimetric and holonomic restrictions. Our results not only provide a generalization to previous results but also give new contributions in fractional variational calculus. Finally, we present some examples to illustrate our results.
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spelling A generalization of a fractional variational problem with dependence on the boundaries and a real parameterFractional calculusEuler–Lagrange equationNatural boundary conditionsIsoperimetric problemsHolonomic-constrained problemsIn this paper, we present a new fractional variational problem where the Lagrangian depends not only on the independent variable, an unknown function and its left- and right-sided Caputo fractional derivatives with respect to another function, but also on the endpoint conditions and a free parameter. The main results of this paper are necessary and sufficient optimality conditions for variational problems with or without isoperimetric and holonomic restrictions. Our results not only provide a generalization to previous results but also give new contributions in fractional variational calculus. Finally, we present some examples to illustrate our results.MDPI2021-03-23T09:39:28Z2021-01-01T00:00:00Z2021info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/30987eng10.3390/fractalfract5010024Almeida, 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:RCAAP2024-02-22T11:59:52Zoai:ria.ua.pt:10773/30987Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:02:58.774749Repositório 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 A generalization of a fractional variational problem with dependence on the boundaries and a real parameter
title A generalization of a fractional variational problem with dependence on the boundaries and a real parameter
spellingShingle A generalization of a fractional variational problem with dependence on the boundaries and a real parameter
Almeida, Ricardo
Fractional calculus
Euler–Lagrange equation
Natural boundary conditions
Isoperimetric problems
Holonomic-constrained problems
title_short A generalization of a fractional variational problem with dependence on the boundaries and a real parameter
title_full A generalization of a fractional variational problem with dependence on the boundaries and a real parameter
title_fullStr A generalization of a fractional variational problem with dependence on the boundaries and a real parameter
title_full_unstemmed A generalization of a fractional variational problem with dependence on the boundaries and a real parameter
title_sort A generalization of a fractional variational problem with dependence on the boundaries 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
Isoperimetric problems
Holonomic-constrained problems
topic Fractional calculus
Euler–Lagrange equation
Natural boundary conditions
Isoperimetric problems
Holonomic-constrained problems
description In this paper, we present a new fractional variational problem where the Lagrangian depends not only on the independent variable, an unknown function and its left- and right-sided Caputo fractional derivatives with respect to another function, but also on the endpoint conditions and a free parameter. The main results of this paper are necessary and sufficient optimality conditions for variational problems with or without isoperimetric and holonomic restrictions. Our results not only provide a generalization to previous results but also give new contributions in fractional variational calculus. Finally, we present some examples to illustrate our results.
publishDate 2021
dc.date.none.fl_str_mv 2021-03-23T09:39:28Z
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
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/30987
url http://hdl.handle.net/10773/30987
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.3390/fractalfract5010024
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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publisher.none.fl_str_mv MDPI
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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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