About Convergence and Order of Convergence of Some Fractional Derivatives

Autores
Roscani, Sabrina Dina; Venturato, Lucas David
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we obtain some convergence results for Riemann-Liouville, Caputo, and Caputo–Fabrizio fractional operators when the order of differentiation approaches one. We consider the errors given by D 1−α f − f ′ p for p=1 and p = ∞ and we prove that for bothm the Caputo and Caputo Fabrizio operators, the order of convergence is a positive real r ∈ (0,1). Finally, we compare the speed of convergence between Caputo and Caputo–Fabrizio operators obtaining that they are related by the Digamma function.
Fil: Roscani, Sabrina Dina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral; Argentina
Fil: Venturato, Lucas David. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
CAPUTO-FABRIZIO DERIVATIVE
CAPUTO DERIVATIVE
ORDER OF CONVERGENCE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/221494
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/221494
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling About Convergence and Order of Convergence of Some Fractional DerivativesRoscani, Sabrina DinaVenturato, Lucas DavidCAPUTO-FABRIZIO DERIVATIVECAPUTO DERIVATIVEORDER OF CONVERGENCEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we obtain some convergence results for Riemann-Liouville, Caputo, and Caputo–Fabrizio fractional operators when the order of differentiation approaches one. We consider the errors given by D 1−α f − f ′ p for p=1 and p = ∞ and we prove that for bothm the Caputo and Caputo Fabrizio operators, the order of convergence is a positive real r ∈ (0,1). Finally, we compare the speed of convergence between Caputo and Caputo–Fabrizio operators obtaining that they are related by the Digamma function.Fil: Roscani, Sabrina Dina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral; ArgentinaFil: Venturato, Lucas David. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaNatural Science Publishing2022-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/221494Roscani, Sabrina Dina; Venturato, Lucas David; About Convergence and Order of Convergence of Some Fractional Derivatives; Natural Science Publishing; Progress in Fractional Differentiation and Applications; 8; 4; 10-2022; 495-5082356-93362356-9344CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.naturalspublishing.com/Article.asp?ArtcID=25816info:eu-repo/semantics/altIdentifier/doi/10.18576/pfda/080404info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:25:20Zoai:ri.conicet.gov.ar:11336/221494instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:25:20.547CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv About Convergence and Order of Convergence of Some Fractional Derivatives
title About Convergence and Order of Convergence of Some Fractional Derivatives
spellingShingle About Convergence and Order of Convergence of Some Fractional Derivatives
Roscani, Sabrina Dina
CAPUTO-FABRIZIO DERIVATIVE
CAPUTO DERIVATIVE
ORDER OF CONVERGENCE
title_short About Convergence and Order of Convergence of Some Fractional Derivatives
title_full About Convergence and Order of Convergence of Some Fractional Derivatives
title_fullStr About Convergence and Order of Convergence of Some Fractional Derivatives
title_full_unstemmed About Convergence and Order of Convergence of Some Fractional Derivatives
title_sort About Convergence and Order of Convergence of Some Fractional Derivatives
dc.creator.none.fl_str_mv Roscani, Sabrina Dina
Venturato, Lucas David
author Roscani, Sabrina Dina
author_facet Roscani, Sabrina Dina
Venturato, Lucas David
author_role author
author2 Venturato, Lucas David
author2_role author
dc.subject.none.fl_str_mv CAPUTO-FABRIZIO DERIVATIVE
CAPUTO DERIVATIVE
ORDER OF CONVERGENCE
topic CAPUTO-FABRIZIO DERIVATIVE
CAPUTO DERIVATIVE
ORDER OF CONVERGENCE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we obtain some convergence results for Riemann-Liouville, Caputo, and Caputo–Fabrizio fractional operators when the order of differentiation approaches one. We consider the errors given by D 1−α f − f ′ p for p=1 and p = ∞ and we prove that for bothm the Caputo and Caputo Fabrizio operators, the order of convergence is a positive real r ∈ (0,1). Finally, we compare the speed of convergence between Caputo and Caputo–Fabrizio operators obtaining that they are related by the Digamma function.
Fil: Roscani, Sabrina Dina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral; Argentina
Fil: Venturato, Lucas David. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this paper we obtain some convergence results for Riemann-Liouville, Caputo, and Caputo–Fabrizio fractional operators when the order of differentiation approaches one. We consider the errors given by D 1−α f − f ′ p for p=1 and p = ∞ and we prove that for bothm the Caputo and Caputo Fabrizio operators, the order of convergence is a positive real r ∈ (0,1). Finally, we compare the speed of convergence between Caputo and Caputo–Fabrizio operators obtaining that they are related by the Digamma function.
publishDate 2022
dc.date.none.fl_str_mv 2022-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/221494
Roscani, Sabrina Dina; Venturato, Lucas David; About Convergence and Order of Convergence of Some Fractional Derivatives; Natural Science Publishing; Progress in Fractional Differentiation and Applications; 8; 4; 10-2022; 495-508
2356-9336
2356-9344
CONICET Digital
CONICET
url http://hdl.handle.net/11336/221494
identifier_str_mv Roscani, Sabrina Dina; Venturato, Lucas David; About Convergence and Order of Convergence of Some Fractional Derivatives; Natural Science Publishing; Progress in Fractional Differentiation and Applications; 8; 4; 10-2022; 495-508
2356-9336
2356-9344
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.naturalspublishing.com/Article.asp?ArtcID=25816
info:eu-repo/semantics/altIdentifier/doi/10.18576/pfda/080404
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Natural Science Publishing
publisher.none.fl_str_mv Natural Science Publishing
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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