The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function

In this paper, we consider the existence of solutions of the nonlinear fractional differential equation boundary-value problem Dα* u(t) = f (t, u(t), u′(t), CDβu(t)), 0 < t < 1, 1 < α < 2, 0 < β ≤ 1, u(0) = A, u(1) = Bu(η), where 0 < η < 1, A ≥ 0, Bη > 1, Dα* is the modified...

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Detalhes bibliográficos
Autores: Aleksic, Suzana, Cabada Fernández, Alberto, Dimitrijevic, Sladjana, Tomovic Mladenovic, Tatjana V.
Formato: artículo
Fecha de publicación:2023
País:España
Recursos:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/39699
Acesso em linha:https://hdl.handle.net/10347/39699
Access Level:acceso abierto
Palavra-chave:Fractional Differential Equations
Green’s Functions
Boundary Value Problem
120215 Ecuaciones integrales
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spelling The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown functionAleksic, SuzanaCabada Fernández, AlbertoDimitrijevic, SladjanaTomovic Mladenovic, Tatjana V.Fractional Differential EquationsGreen’s FunctionsBoundary Value Problem120215 Ecuaciones integralesIn this paper, we consider the existence of solutions of the nonlinear fractional differential equation boundary-value problem Dα* u(t) = f (t, u(t), u′(t), CDβu(t)), 0 < t < 1, 1 < α < 2, 0 < β ≤ 1, u(0) = A, u(1) = Bu(η), where 0 < η < 1, A ≥ 0, Bη > 1, Dα* is the modified Caputo fractional derivative of order α, CDβ is the Caputo fractional derivative of order β, and f is a function in C([0, 1] × R × R × R). Existence results for a solution are obtained. Two examples are presented to illustrate the results.Faculty of Sciences and Mathematics, University of Nis, SerbiaUniversidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización20232023-01-0120232023-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10347/39699reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113275GB-I00 ECUACIONES DIFERENCIALES ORDINARIAS NO LINEALES Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:minerva.usc.gal:10347/396992026-06-15T12:47:27Z
dc.title.none.fl_str_mv The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function
title The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function
spellingShingle The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function
Aleksic, Suzana
Fractional Differential Equations
Green’s Functions
Boundary Value Problem
120215 Ecuaciones integrales
title_short The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function
title_full The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function
title_fullStr The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function
title_full_unstemmed The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function
title_sort The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function
dc.creator.none.fl_str_mv Aleksic, Suzana
Cabada Fernández, Alberto
Dimitrijevic, Sladjana
Tomovic Mladenovic, Tatjana V.
author Aleksic, Suzana
author_facet Aleksic, Suzana
Cabada Fernández, Alberto
Dimitrijevic, Sladjana
Tomovic Mladenovic, Tatjana V.
author_role author
author2 Cabada Fernández, Alberto
Dimitrijevic, Sladjana
Tomovic Mladenovic, Tatjana V.
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
dc.subject.none.fl_str_mv Fractional Differential Equations
Green’s Functions
Boundary Value Problem
120215 Ecuaciones integrales
topic Fractional Differential Equations
Green’s Functions
Boundary Value Problem
120215 Ecuaciones integrales
description In this paper, we consider the existence of solutions of the nonlinear fractional differential equation boundary-value problem Dα* u(t) = f (t, u(t), u′(t), CDβu(t)), 0 < t < 1, 1 < α < 2, 0 < β ≤ 1, u(0) = A, u(1) = Bu(η), where 0 < η < 1, A ≥ 0, Bη > 1, Dα* is the modified Caputo fractional derivative of order α, CDβ is the Caputo fractional derivative of order β, and f is a function in C([0, 1] × R × R × R). Existence results for a solution are obtained. Two examples are presented to illustrate the results.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-01-01
2023
2023-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10347/39699
url https://hdl.handle.net/10347/39699
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113275GB-I00 ECUACIONES DIFERENCIALES ORDINARIAS NO LINEALES Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Faculty of Sciences and Mathematics, University of Nis, Serbia
publisher.none.fl_str_mv Faculty of Sciences and Mathematics, University of Nis, Serbia
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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