Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernel

[EN] Fractional stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm) have attracted growing attention due to their ability to model systems exhibiting non-Markovian dynamics and long-range dependence, which naturally arise in many real-world phenomena characterized by...

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Autores: Liaqat, Muhammad Imran, Akgul, Ali, Conejero, J. Alberto|||0000-0003-3681-7533
Formato: artículo
Fecha de publicación:2026
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:dnet:riunet______::035de99ea4ab0fdb21f8637a0ea54d1d
Acesso em linha:https://riunet.upv.es/handle/10251/233489
Access Level:acceso abierto
Palavra-chave:Ffractional Brownian motion
Mild solutions
Picard iteration approach
Fixed point approach
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spelling Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernelLiaqat, Muhammad ImranAkgul, AliConejero, J. Alberto|||0000-0003-3681-7533Ffractional Brownian motionMild solutionsPicard iteration approachFixed point approach[EN] Fractional stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm) have attracted growing attention due to their ability to model systems exhibiting non-Markovian dynamics and long-range dependence, which naturally arise in many real-world phenomena characterized by hereditary and persistent randomness. In this work, we establish the existence and uniqueness of mild solutions using the Picard iteration technique for the case where the Hurst parameter (1 ) satisfies H is an element of 2, 1 . Moreover, we establish the approximate controllability of the systems under suitable conditions. To generalize the theoretical framework, we employ the Caputo-Katugampola fractional derivative (CKFD), thereby extending the analysis to a broader class of fractional stochastic systems.Prof. J.A.C. is supported by Generalitat Valenciana, Project PROMETEO CIPROM/2022/21.American Institute of Mathematical SciencesDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería InformáticaGeneralitat ValencianaRepositorio Institucional de la Universitat Politècnica de València Riunet20262026-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/233489reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 CIPROM%2F2022%2F21open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:dnet:riunet______::035de99ea4ab0fdb21f8637a0ea54d1d2026-06-13T07:49:27Z
dc.title.none.fl_str_mv Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernel
title Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernel
spellingShingle Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernel
Liaqat, Muhammad Imran
Ffractional Brownian motion
Mild solutions
Picard iteration approach
Fixed point approach
title_short Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernel
title_full Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernel
title_fullStr Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernel
title_full_unstemmed Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernel
title_sort Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernel
dc.creator.none.fl_str_mv Liaqat, Muhammad Imran
Akgul, Ali
Conejero, J. Alberto|||0000-0003-3681-7533
author Liaqat, Muhammad Imran
author_facet Liaqat, Muhammad Imran
Akgul, Ali
Conejero, J. Alberto|||0000-0003-3681-7533
author_role author
author2 Akgul, Ali
Conejero, J. Alberto|||0000-0003-3681-7533
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Informática
Generalitat Valenciana
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Ffractional Brownian motion
Mild solutions
Picard iteration approach
Fixed point approach
topic Ffractional Brownian motion
Mild solutions
Picard iteration approach
Fixed point approach
description [EN] Fractional stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm) have attracted growing attention due to their ability to model systems exhibiting non-Markovian dynamics and long-range dependence, which naturally arise in many real-world phenomena characterized by hereditary and persistent randomness. In this work, we establish the existence and uniqueness of mild solutions using the Picard iteration technique for the case where the Hurst parameter (1 ) satisfies H is an element of 2, 1 . Moreover, we establish the approximate controllability of the systems under suitable conditions. To generalize the theoretical framework, we employ the Caputo-Katugampola fractional derivative (CKFD), thereby extending the analysis to a broader class of fractional stochastic systems.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-01-01
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://riunet.upv.es/handle/10251/233489
url https://riunet.upv.es/handle/10251/233489
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Generalitat Valenciana https://doi.org/10.13039/501100003359 CIPROM%2F2022%2F21
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/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
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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