Existência de solução para um problema envolvendo uma equação diferencial fracionária
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional Manancial UFSM |
Texto Completo: | http://repositorio.ufsm.br/handle/1/20927 |
Resumo: | This paper aims to present results that guarantee the existence of solution to a problem involving a fractional differential equation with antiperiodic boundary conditions. The fractional differential equation considered in such a problem is given in terms of the Caputo fractional derivative. To ensure the validity of the results, we make use of the theory of Leray-Schauder topological degree, and fixed point theorems, namely Altman’s fixed point theorem and Schauder’s fixed point theorem, which are also demonstrated with the aid of properties from the Leray-Schauder topological degree. |
id |
UFSM-20_df7f4fdcdbbedc03abda1982dd131b24 |
---|---|
oai_identifier_str |
oai:repositorio.ufsm.br:1/20927 |
network_acronym_str |
UFSM-20 |
network_name_str |
Repositório Institucional Manancial UFSM |
repository_id_str |
3913 |
spelling |
2021-05-19T17:20:11Z2021-05-19T17:20:11Z2019-11-06http://repositorio.ufsm.br/handle/1/20927This paper aims to present results that guarantee the existence of solution to a problem involving a fractional differential equation with antiperiodic boundary conditions. The fractional differential equation considered in such a problem is given in terms of the Caputo fractional derivative. To ensure the validity of the results, we make use of the theory of Leray-Schauder topological degree, and fixed point theorems, namely Altman’s fixed point theorem and Schauder’s fixed point theorem, which are also demonstrated with the aid of properties from the Leray-Schauder topological degree.Este trabalho tem por objetivo apresentar resultados que garantem a existência de solução para um problema envolvendo uma equação diferencial fracionária com condições de contorno antiperiódicas. A equação diferencial fracionária considerada em tal problema, é dada em termos da derivada fracionária de Caputo. Para garantirmos a validade dos resultados, fazemos uso da teoria do grau topológico de Leray-Schauder, e de teoremas do ponto fixo, a saber, o Teorema do ponto fixo de Altman e o Teorema do ponto fixo de Schauder, que são também demonstrados, com o auxílio de propriedades provenientes do grau topológico de Leray-Schauder.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade Federal de Santa MariaCentro de Ciências Naturais e ExatasPrograma de Pós-Graduação em MatemáticaUFSMBrasilMatemáticaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessEquação diferencial fracionáriaDerivada fracionária de CaputoGrau topológico de Leray-SchauderTeorema do ponto fixo de AltmanTeorema do ponto fixo de SchauderFractional differential equationCaputo fractional derivativeLeray-Schauder topological degreeAltman’s fixed point theoremSchauder’s fixed point theoremCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAExistência de solução para um problema envolvendo uma equação diferencial fracionáriaExistence of solution for a problem involving a fractional differential equationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisMiotto, Taísa Jungeshttp://lattes.cnpq.br/3442278498547366Martins, Claudete Matilde WeblerXXXXXXXXXXXXXXXBuriol, CeleneXXXXXXXXXXXXXXhttp://lattes.cnpq.br/4764844172818891Forsch, Fabíola Cristiane100100000008600e7cf3d6e-5fab-4115-b82f-4bb25fee6400146b5799-2d49-461c-8d7a-af4c14c814d7acd87e43-f76a-47b1-a3e3-e1e9025b4a527d66b293-9f4c-4fcb-b2ce-c8d018b75443reponame:Repositório Institucional Manancial UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMORIGINALDIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdfDIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdfDissertação de Mestradoapplication/pdf721292http://repositorio.ufsm.br/bitstream/1/20927/1/DIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdfe3bb304128178945a94f82e4a388a48bMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.ufsm.br/bitstream/1/20927/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81956http://repositorio.ufsm.br/bitstream/1/20927/3/license.txt2f0571ecee68693bd5cd3f17c1e075dfMD53TEXTDIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdf.txtDIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdf.txtExtracted texttext/plain141317http://repositorio.ufsm.br/bitstream/1/20927/4/DIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdf.txt4b7a9c296536fa4c00816f0fda275f11MD54THUMBNAILDIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdf.jpgDIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdf.jpgIM Thumbnailimage/jpeg4280http://repositorio.ufsm.br/bitstream/1/20927/5/DIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdf.jpg8c1025c3bd2757f98c6d393373b7d0b2MD551/209272021-05-20 03:02:13.001oai:repositorio.ufsm.br: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ório Institucionalhttp://repositorio.ufsm.br/PUBhttp://repositorio.ufsm.br/oai/requestouvidoria@ufsm.bropendoar:39132021-05-20T06:02:13Repositório Institucional Manancial UFSM - Universidade Federal de Santa Maria (UFSM)false |
dc.title.por.fl_str_mv |
Existência de solução para um problema envolvendo uma equação diferencial fracionária |
dc.title.alternative.eng.fl_str_mv |
Existence of solution for a problem involving a fractional differential equation |
title |
Existência de solução para um problema envolvendo uma equação diferencial fracionária |
spellingShingle |
Existência de solução para um problema envolvendo uma equação diferencial fracionária Forsch, Fabíola Cristiane Equação diferencial fracionária Derivada fracionária de Caputo Grau topológico de Leray-Schauder Teorema do ponto fixo de Altman Teorema do ponto fixo de Schauder Fractional differential equation Caputo fractional derivative Leray-Schauder topological degree Altman’s fixed point theorem Schauder’s fixed point theorem CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Existência de solução para um problema envolvendo uma equação diferencial fracionária |
title_full |
Existência de solução para um problema envolvendo uma equação diferencial fracionária |
title_fullStr |
Existência de solução para um problema envolvendo uma equação diferencial fracionária |
title_full_unstemmed |
Existência de solução para um problema envolvendo uma equação diferencial fracionária |
title_sort |
Existência de solução para um problema envolvendo uma equação diferencial fracionária |
author |
Forsch, Fabíola Cristiane |
author_facet |
Forsch, Fabíola Cristiane |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Miotto, Taísa Junges |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/3442278498547366 |
dc.contributor.referee1.fl_str_mv |
Martins, Claudete Matilde Webler |
dc.contributor.referee1Lattes.fl_str_mv |
XXXXXXXXXXXXXXX |
dc.contributor.referee2.fl_str_mv |
Buriol, Celene |
dc.contributor.referee2Lattes.fl_str_mv |
XXXXXXXXXXXXXX |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/4764844172818891 |
dc.contributor.author.fl_str_mv |
Forsch, Fabíola Cristiane |
contributor_str_mv |
Miotto, Taísa Junges Martins, Claudete Matilde Webler Buriol, Celene |
dc.subject.por.fl_str_mv |
Equação diferencial fracionária Derivada fracionária de Caputo Grau topológico de Leray-Schauder Teorema do ponto fixo de Altman Teorema do ponto fixo de Schauder |
topic |
Equação diferencial fracionária Derivada fracionária de Caputo Grau topológico de Leray-Schauder Teorema do ponto fixo de Altman Teorema do ponto fixo de Schauder Fractional differential equation Caputo fractional derivative Leray-Schauder topological degree Altman’s fixed point theorem Schauder’s fixed point theorem CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Fractional differential equation Caputo fractional derivative Leray-Schauder topological degree Altman’s fixed point theorem Schauder’s fixed point theorem |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This paper aims to present results that guarantee the existence of solution to a problem involving a fractional differential equation with antiperiodic boundary conditions. The fractional differential equation considered in such a problem is given in terms of the Caputo fractional derivative. To ensure the validity of the results, we make use of the theory of Leray-Schauder topological degree, and fixed point theorems, namely Altman’s fixed point theorem and Schauder’s fixed point theorem, which are also demonstrated with the aid of properties from the Leray-Schauder topological degree. |
publishDate |
2019 |
dc.date.issued.fl_str_mv |
2019-11-06 |
dc.date.accessioned.fl_str_mv |
2021-05-19T17:20:11Z |
dc.date.available.fl_str_mv |
2021-05-19T17:20:11Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://repositorio.ufsm.br/handle/1/20927 |
url |
http://repositorio.ufsm.br/handle/1/20927 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.cnpq.fl_str_mv |
100100000008 |
dc.relation.confidence.fl_str_mv |
600 |
dc.relation.authority.fl_str_mv |
e7cf3d6e-5fab-4115-b82f-4bb25fee6400 146b5799-2d49-461c-8d7a-af4c14c814d7 acd87e43-f76a-47b1-a3e3-e1e9025b4a52 7d66b293-9f4c-4fcb-b2ce-c8d018b75443 |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Centro de Ciências Naturais e Exatas |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Matemática |
dc.publisher.initials.fl_str_mv |
UFSM |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Matemática |
publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Centro de Ciências Naturais e Exatas |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional Manancial UFSM instname:Universidade Federal de Santa Maria (UFSM) instacron:UFSM |
instname_str |
Universidade Federal de Santa Maria (UFSM) |
instacron_str |
UFSM |
institution |
UFSM |
reponame_str |
Repositório Institucional Manancial UFSM |
collection |
Repositório Institucional Manancial UFSM |
bitstream.url.fl_str_mv |
http://repositorio.ufsm.br/bitstream/1/20927/1/DIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdf http://repositorio.ufsm.br/bitstream/1/20927/2/license_rdf http://repositorio.ufsm.br/bitstream/1/20927/3/license.txt http://repositorio.ufsm.br/bitstream/1/20927/4/DIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdf.txt http://repositorio.ufsm.br/bitstream/1/20927/5/DIS_PPGMATEMATICA_2019_FORSCH_FABIOLA.pdf.jpg |
bitstream.checksum.fl_str_mv |
e3bb304128178945a94f82e4a388a48b 4460e5956bc1d1639be9ae6146a50347 2f0571ecee68693bd5cd3f17c1e075df 4b7a9c296536fa4c00816f0fda275f11 8c1025c3bd2757f98c6d393373b7d0b2 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional Manancial UFSM - Universidade Federal de Santa Maria (UFSM) |
repository.mail.fl_str_mv |
ouvidoria@ufsm.br |
_version_ |
1808854704226041856 |