Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions

Bibliographic Details
Main Author: Debbouche, Amar
Publication Date: 2015
Other Authors: Torres, Delfim F. M.
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/15036
Summary: 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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spelling 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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T03:55:54Zoai:ria.ua.pt:10773/15036Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:51:23.316481Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
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
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dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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