Well-posedness and qualitative properties for abstract time-difference equations

In this thesis we introduce the notions of the stable Levy process and the scaled Wright function within the discrete setting. Using these notions, we prove a subordination principle which will be used to investigate different classes of discrete time fractional difference equations. In addition, we...

Full description

Autores:
Díaz Noguera, Stiven E.
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2021
Institución:
Universidad del Norte
Repositorio:
Repositorio Uninorte
Idioma:
eng
OAI Identifier:
oai:manglar.uninorte.edu.co:10584/10075
Acceso en línea:
http://hdl.handle.net/10584/10075
Palabra clave:
Ecuaciones diferenciales
Ecuaciones diferenciales fraccionarias
Rights
openAccess
License
https://creativecommons.org/licenses/by/4.0/
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spelling Álvarez, EdgardoLizama, CarlosDíaz Noguera, Stiven E.2022-02-25T22:04:42Z2022-02-25T22:04:42Z2021http://hdl.handle.net/10584/10075In this thesis we introduce the notions of the stable Levy process and the scaled Wright function within the discrete setting. Using these notions, we prove a subordination principle which will be used to investigate different classes of discrete time fractional difference equations. In addition, we introduce the Banach space of (N, λ)-periodic vector-valued sequences. Moreover, we show the existence and uniqueness of (N, λ)-periodic solutions to a class of abstract Volterra difference equations as well as of fractional difference equations.DoctoradoDoctor en Ciencias Naturalesapplication/pdfengUniversidad del NorteDoctorado en Ciencias NaturalesDepartamento de física y geocienciasBarranquilla, ColombiaWell-posedness and qualitative properties for abstract time-difference equationsTrabajo de grado - Doctoradohttp://purl.org/coar/resource_type/c_db06info:eu-repo/semantics/doctoralThesisTexthttp://purl.org/coar/version/c_dc82b40f9837b551https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Ecuaciones diferencialesEcuaciones diferenciales fraccionariasEstudiantesDoctoradoORIGINAL1129507652.pdf1129507652.pdfapplication/pdf717747https://manglar.uninorte.edu.co/bitstream/10584/10075/1/1129507652.pdfa588dbf145fa1e7896459d4cc31ea248MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://manglar.uninorte.edu.co/bitstream/10584/10075/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5210584/10075oai:manglar.uninorte.edu.co:10584/100752022-02-25 17:04:42.398Repositorio Digital de la Universidad del Nortemauribe@uninorte.edu.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
dc.title.es_ES.fl_str_mv Well-posedness and qualitative properties for abstract time-difference equations
title Well-posedness and qualitative properties for abstract time-difference equations
spellingShingle Well-posedness and qualitative properties for abstract time-difference equations
Ecuaciones diferenciales
Ecuaciones diferenciales fraccionarias
title_short Well-posedness and qualitative properties for abstract time-difference equations
title_full Well-posedness and qualitative properties for abstract time-difference equations
title_fullStr Well-posedness and qualitative properties for abstract time-difference equations
title_full_unstemmed Well-posedness and qualitative properties for abstract time-difference equations
title_sort Well-posedness and qualitative properties for abstract time-difference equations
dc.creator.fl_str_mv Díaz Noguera, Stiven E.
dc.contributor.advisor.none.fl_str_mv Álvarez, Edgardo
Lizama, Carlos
dc.contributor.author.none.fl_str_mv Díaz Noguera, Stiven E.
dc.subject.lemb.none.fl_str_mv Ecuaciones diferenciales
Ecuaciones diferenciales fraccionarias
topic Ecuaciones diferenciales
Ecuaciones diferenciales fraccionarias
description In this thesis we introduce the notions of the stable Levy process and the scaled Wright function within the discrete setting. Using these notions, we prove a subordination principle which will be used to investigate different classes of discrete time fractional difference equations. In addition, we introduce the Banach space of (N, λ)-periodic vector-valued sequences. Moreover, we show the existence and uniqueness of (N, λ)-periodic solutions to a class of abstract Volterra difference equations as well as of fractional difference equations.
publishDate 2021
dc.date.issued.none.fl_str_mv 2021
dc.date.accessioned.none.fl_str_mv 2022-02-25T22:04:42Z
dc.date.available.none.fl_str_mv 2022-02-25T22:04:42Z
dc.type.es_ES.fl_str_mv Trabajo de grado - Doctorado
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_dc82b40f9837b551
dc.type.coar.es_ES.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.driver.es_ES.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.content.es_ES.fl_str_mv Text
format http://purl.org/coar/resource_type/c_db06
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10584/10075
url http://hdl.handle.net/10584/10075
dc.language.iso.es_ES.fl_str_mv eng
language eng
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.creativecommons.es_ES.fl_str_mv https://creativecommons.org/licenses/by/4.0/
dc.rights.accessrights.es_ES.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.es_ES.fl_str_mv application/pdf
dc.publisher.es_ES.fl_str_mv Universidad del Norte
dc.publisher.program.es_ES.fl_str_mv Doctorado en Ciencias Naturales
dc.publisher.department.es_ES.fl_str_mv Departamento de física y geociencias
dc.publisher.place.es_ES.fl_str_mv Barranquilla, Colombia
institution Universidad del Norte
bitstream.url.fl_str_mv https://manglar.uninorte.edu.co/bitstream/10584/10075/1/1129507652.pdf
https://manglar.uninorte.edu.co/bitstream/10584/10075/2/license.txt
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bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
repository.name.fl_str_mv Repositorio Digital de la Universidad del Norte
repository.mail.fl_str_mv mauribe@uninorte.edu.co
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