Caputo fractional differential equation with state dependent delay and practical stability
Autor(a) principal: | |
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Data de Publicação: | 2019 |
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/10773/26362 |
Resumo: | Practical stability properties of Caputo fractional delay differential equations is studied and, in particular, the case with state dependent delays is considered. These type of delays is a generalization of several types of delays such as constant delays, time variable delays, or distributed delays. In connection with the presence of a delay in a fractional differential equation and the application of the fractional generalization of the Razumikhin method, we give a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. Three types of derivatives for Lyapunov functions, the Caputo fractional derivative, the Dini fractional derivative, and the Caputo fractional Dini derivative, are applied to obtain several sufficient conditions for practical stability. An appropriate Razumikhin condition is applied. These derivatives allow the application of non-quadratic Lyapunov function for studying stability properties. We illustrate our theory on several nonlinear Caputo fractional differential equations with different types of delays |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Caputo fractional differential equation with state dependent delay and practical stabilityFunctional-differential equations with fractional derivativesStabilityLyapunov functionsState dependent delayPractical stability properties of Caputo fractional delay differential equations is studied and, in particular, the case with state dependent delays is considered. These type of delays is a generalization of several types of delays such as constant delays, time variable delays, or distributed delays. In connection with the presence of a delay in a fractional differential equation and the application of the fractional generalization of the Razumikhin method, we give a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. Three types of derivatives for Lyapunov functions, the Caputo fractional derivative, the Dini fractional derivative, and the Caputo fractional Dini derivative, are applied to obtain several sufficient conditions for practical stability. An appropriate Razumikhin condition is applied. These derivatives allow the application of non-quadratic Lyapunov function for studying stability properties. We illustrate our theory on several nonlinear Caputo fractional differential equations with different types of delaysDynamic Publishers, Inc2019-08-01T14:44:59Z2019-01-01T00:00:00Z2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/26362eng1056-217610.12732/dsa.v28i3.11Agarwal, RaviAlmeida, RicardoHristova, SnezhanaO'Regan, Donalinfo: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:RCAAP2024-02-22T11:51:00Zoai:ria.ua.pt:10773/26362Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:59:21.537016Repositório 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 |
Caputo fractional differential equation with state dependent delay and practical stability |
title |
Caputo fractional differential equation with state dependent delay and practical stability |
spellingShingle |
Caputo fractional differential equation with state dependent delay and practical stability Agarwal, Ravi Functional-differential equations with fractional derivatives Stability Lyapunov functions State dependent delay |
title_short |
Caputo fractional differential equation with state dependent delay and practical stability |
title_full |
Caputo fractional differential equation with state dependent delay and practical stability |
title_fullStr |
Caputo fractional differential equation with state dependent delay and practical stability |
title_full_unstemmed |
Caputo fractional differential equation with state dependent delay and practical stability |
title_sort |
Caputo fractional differential equation with state dependent delay and practical stability |
author |
Agarwal, Ravi |
author_facet |
Agarwal, Ravi Almeida, Ricardo Hristova, Snezhana O'Regan, Donal |
author_role |
author |
author2 |
Almeida, Ricardo Hristova, Snezhana O'Regan, Donal |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Agarwal, Ravi Almeida, Ricardo Hristova, Snezhana O'Regan, Donal |
dc.subject.por.fl_str_mv |
Functional-differential equations with fractional derivatives Stability Lyapunov functions State dependent delay |
topic |
Functional-differential equations with fractional derivatives Stability Lyapunov functions State dependent delay |
description |
Practical stability properties of Caputo fractional delay differential equations is studied and, in particular, the case with state dependent delays is considered. These type of delays is a generalization of several types of delays such as constant delays, time variable delays, or distributed delays. In connection with the presence of a delay in a fractional differential equation and the application of the fractional generalization of the Razumikhin method, we give a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. Three types of derivatives for Lyapunov functions, the Caputo fractional derivative, the Dini fractional derivative, and the Caputo fractional Dini derivative, are applied to obtain several sufficient conditions for practical stability. An appropriate Razumikhin condition is applied. These derivatives allow the application of non-quadratic Lyapunov function for studying stability properties. We illustrate our theory on several nonlinear Caputo fractional differential equations with different types of delays |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-08-01T14:44:59Z 2019-01-01T00:00:00Z 2019 |
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/10773/26362 |
url |
http://hdl.handle.net/10773/26362 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1056-2176 10.12732/dsa.v28i3.11 |
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 |
Dynamic Publishers, Inc |
publisher.none.fl_str_mv |
Dynamic Publishers, Inc |
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 |
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1799137648314417152 |