Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications

Detalhes bibliográficos
Autor(a) principal: Almeida, Ricardo
Data de Publicação: 2018
Outros Autores: Malinowska, Agnieszka B., Monteiro, M. Teresa T.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/60586
Resumo: This paper is devoted to the study of the initial value problem of nonlinear fractional differential equations involving a Caputo-type fractional derivative with respect to another function. Existence and uniqueness results for the problem are established by means of the some standard fixed point theorems. Next, we develop the Picard iteration method for solving numerically the problem and obtain results on the long-term behavior of solutions. Finally, we analyze a population growth model and a gross domestic product model with governing equations being fractional differential equations that we have introduced in this work.
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spelling Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applicationsFractional calculusFractional differential equationsPopulation growth modelGross domestic product modelScience & TechnologyThis paper is devoted to the study of the initial value problem of nonlinear fractional differential equations involving a Caputo-type fractional derivative with respect to another function. Existence and uniqueness results for the problem are established by means of the some standard fixed point theorems. Next, we develop the Picard iteration method for solving numerically the problem and obtain results on the long-term behavior of solutions. Finally, we analyze a population growth model and a gross domestic product model with governing equations being fractional differential equations that we have introduced in this work.R. Almeida was supported by Portuguese funds through the CIDMA-Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UID/MAT/04106/2013; A. B. Malinowska by the Bialystok University of Technology grant S/WI/1/2016, and M. T. Monteiro by COMPETE: POCI-01-0145-FEDER-007043 and FCT-Fundação para a Ciência e a Tecnologia within the Project Scope: UID/CEC/00319/2013.info:eu-repo/semantics/publishedVersionWileyUniversidade do MinhoAlmeida, RicardoMalinowska, Agnieszka B.Monteiro, M. Teresa T.20182018-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/60586eng0170-42141099-147610.1002/mma.4617info: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:RCAAP2023-07-21T12:08:33Zoai:repositorium.sdum.uminho.pt:1822/60586Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:59:47.028037Repositório 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 Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
title Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
spellingShingle Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
Almeida, Ricardo
Fractional calculus
Fractional differential equations
Population growth model
Gross domestic product model
Science & Technology
title_short Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
title_full Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
title_fullStr Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
title_full_unstemmed Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
title_sort Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
author Almeida, Ricardo
author_facet Almeida, Ricardo
Malinowska, Agnieszka B.
Monteiro, M. Teresa T.
author_role author
author2 Malinowska, Agnieszka B.
Monteiro, M. Teresa T.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Almeida, Ricardo
Malinowska, Agnieszka B.
Monteiro, M. Teresa T.
dc.subject.por.fl_str_mv Fractional calculus
Fractional differential equations
Population growth model
Gross domestic product model
Science & Technology
topic Fractional calculus
Fractional differential equations
Population growth model
Gross domestic product model
Science & Technology
description This paper is devoted to the study of the initial value problem of nonlinear fractional differential equations involving a Caputo-type fractional derivative with respect to another function. Existence and uniqueness results for the problem are established by means of the some standard fixed point theorems. Next, we develop the Picard iteration method for solving numerically the problem and obtain results on the long-term behavior of solutions. Finally, we analyze a population growth model and a gross domestic product model with governing equations being fractional differential equations that we have introduced in this work.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01T00:00:00Z
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/1822/60586
url http://hdl.handle.net/1822/60586
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0170-4214
1099-1476
10.1002/mma.4617
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 Wiley
publisher.none.fl_str_mv Wiley
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
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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
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