Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives

Detalhes bibliográficos
Autor(a) principal: Zguaid, Khalid
Data de Publicação: 2023
Outros Autores: El Alaoui, Fatima-Zahrae, Torres, Delfim F. M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/39324
Resumo: We investigate the regional gradient observability of fractional sub-diffusion equations involving the Caputo derivative. The problem consists of describing a method to find and recover the initial gradient vector in the desired region, which is contained in the spatial domain. After giving necessary notions and definitions, we prove some useful characterizations for exact and approximate regional gradient observability. An example of a fractional system that is not (globally) gradient observable but it is regionally gradient observable is given, showing the importance of regional analysis. Our characterization of the notion of regional gradient observability is given for two types of strategic sensors. The recovery of the initial gradient is carried out using an expansion of the Hilbert uniqueness method. Two illustrative examples are given to show the application of the developed approach. The numerical simulations confirm that the proposed algorithm is effective in terms of the reconstruction error.
id RCAP_2c3bdfc5051743a51e9a869550710ae4
oai_identifier_str oai:ria.ua.pt:10773/39324
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Regional gradient observability for fractional differential equations with Caputo time-fractional derivativesDistributed parameter systemsControl theoryFractional calculusRegional analysisGradient observabilityGradient strategic sensorsWe investigate the regional gradient observability of fractional sub-diffusion equations involving the Caputo derivative. The problem consists of describing a method to find and recover the initial gradient vector in the desired region, which is contained in the spatial domain. After giving necessary notions and definitions, we prove some useful characterizations for exact and approximate regional gradient observability. An example of a fractional system that is not (globally) gradient observable but it is regionally gradient observable is given, showing the importance of regional analysis. Our characterization of the notion of regional gradient observability is given for two types of strategic sensors. The recovery of the initial gradient is carried out using an expansion of the Hilbert uniqueness method. Two illustrative examples are given to show the application of the developed approach. The numerical simulations confirm that the proposed algorithm is effective in terms of the reconstruction error.Springer2023-09-06T16:26:18Z2023-01-01T00:00:00Z2023info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/39324eng2195-268X10.1007/s40435-022-01106-0Zguaid, KhalidEl Alaoui, Fatima-ZahraeTorres, 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:RCAAP2024-02-22T12:16:42Zoai:ria.ua.pt:10773/39324Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:09:29.537526Repositório 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 Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives
title Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives
spellingShingle Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives
Zguaid, Khalid
Distributed parameter systems
Control theory
Fractional calculus
Regional analysis
Gradient observability
Gradient strategic sensors
title_short Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives
title_full Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives
title_fullStr Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives
title_full_unstemmed Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives
title_sort Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives
author Zguaid, Khalid
author_facet Zguaid, Khalid
El Alaoui, Fatima-Zahrae
Torres, Delfim F. M.
author_role author
author2 El Alaoui, Fatima-Zahrae
Torres, Delfim F. M.
author2_role author
author
dc.contributor.author.fl_str_mv Zguaid, Khalid
El Alaoui, Fatima-Zahrae
Torres, Delfim F. M.
dc.subject.por.fl_str_mv Distributed parameter systems
Control theory
Fractional calculus
Regional analysis
Gradient observability
Gradient strategic sensors
topic Distributed parameter systems
Control theory
Fractional calculus
Regional analysis
Gradient observability
Gradient strategic sensors
description We investigate the regional gradient observability of fractional sub-diffusion equations involving the Caputo derivative. The problem consists of describing a method to find and recover the initial gradient vector in the desired region, which is contained in the spatial domain. After giving necessary notions and definitions, we prove some useful characterizations for exact and approximate regional gradient observability. An example of a fractional system that is not (globally) gradient observable but it is regionally gradient observable is given, showing the importance of regional analysis. Our characterization of the notion of regional gradient observability is given for two types of strategic sensors. The recovery of the initial gradient is carried out using an expansion of the Hilbert uniqueness method. Two illustrative examples are given to show the application of the developed approach. The numerical simulations confirm that the proposed algorithm is effective in terms of the reconstruction error.
publishDate 2023
dc.date.none.fl_str_mv 2023-09-06T16:26:18Z
2023-01-01T00:00:00Z
2023
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/10773/39324
url http://hdl.handle.net/10773/39324
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2195-268X
10.1007/s40435-022-01106-0
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
publisher.none.fl_str_mv Springer
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
_version_ 1799137745498537984

Registros relacionados