Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions
Autor(a) principal: | |
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Data de Publicação: | 2015 |
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/10773/15036 |
Resumo: | We prove existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal condition is considered in terms of a Riemann-Liouville fractional derivative. A Lagrange optimal control problem is considered, and existence of a multi-integral solution obtained. Main tools include fractional calculus, semigroup theory, fractional power of operators, a singular version of Gronwall's inequality, and Leray-Schauder fixed point theorem. An example illustrating the theory is given. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditionsSobolev type equationsFractional evolution equationsOptimal controlNonlocal conditionsMild solutionsWe prove existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal condition is considered in terms of a Riemann-Liouville fractional derivative. A Lagrange optimal control problem is considered, and existence of a multi-integral solution obtained. Main tools include fractional calculus, semigroup theory, fractional power of operators, a singular version of Gronwall's inequality, and Leray-Schauder fixed point theorem. An example illustrating the theory is given.Springer Verlag2018-07-20T14:00:51Z2015-02-01T00:00:00Z2015-022016-02-01T14:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15036eng1311-045410.1515/fca-2015-0007Debbouche, AmarTorres, Delfim F. M.info: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:RCAAP2024-02-22T11:27:45Zoai:ria.ua.pt:10773/15036Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:29.446814Repositório 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 |
Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions |
title |
Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions |
spellingShingle |
Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions Debbouche, Amar Sobolev type equations Fractional evolution equations Optimal control Nonlocal conditions Mild solutions |
title_short |
Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions |
title_full |
Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions |
title_fullStr |
Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions |
title_full_unstemmed |
Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions |
title_sort |
Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions |
author |
Debbouche, Amar |
author_facet |
Debbouche, Amar Torres, Delfim F. M. |
author_role |
author |
author2 |
Torres, Delfim F. M. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Debbouche, Amar Torres, Delfim F. M. |
dc.subject.por.fl_str_mv |
Sobolev type equations Fractional evolution equations Optimal control Nonlocal conditions Mild solutions |
topic |
Sobolev type equations Fractional evolution equations Optimal control Nonlocal conditions Mild solutions |
description |
We prove existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal condition is considered in terms of a Riemann-Liouville fractional derivative. A Lagrange optimal control problem is considered, and existence of a multi-integral solution obtained. Main tools include fractional calculus, semigroup theory, fractional power of operators, a singular version of Gronwall's inequality, and Leray-Schauder fixed point theorem. An example illustrating the theory is given. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-02-01T00:00:00Z 2015-02 2016-02-01T14:00:00Z 2018-07-20T14:00:51Z |
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/10773/15036 |
url |
http://hdl.handle.net/10773/15036 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1311-0454 10.1515/fca-2015-0007 |
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 |
Springer Verlag |
publisher.none.fl_str_mv |
Springer Verlag |
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 |
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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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1799137555105447936 |