Truncated ��-fractional Taylor’s Formula with Applications

Detalhes bibliográficos
Autor(a) principal: SOUSA,J.V.C.
Data de Publicação: 2018
Outros Autores: OLIVEIRA,E.C.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300525
Resumo: ABSTRACT In this paper, we present and prove a new truncated �� -fractional Taylor’s formula using the truncated �� -fractional variation of constants formula. In this sense, we present the truncated �� -fractional Taylor’s remainder by means of �� -fractional integral, essential for analyzing and comparing the error, when approaching functions by polynomials. From these new results, some applications were made involving some inequalities, specifically, we generalize the Cauchy-Schwartz inequality.
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spelling Truncated ��-fractional Taylor’s Formula with ApplicationsTruncated �� -fractional derivativemultivariable truncated �� -fractional derivativetruncated �� -fractional partial derivativetruncated �� -fractional Jacobian matrixtruncated �� -fractional Green’s theoremABSTRACT In this paper, we present and prove a new truncated �� -fractional Taylor’s formula using the truncated �� -fractional variation of constants formula. In this sense, we present the truncated �� -fractional Taylor’s remainder by means of �� -fractional integral, essential for analyzing and comparing the error, when approaching functions by polynomials. From these new results, some applications were made involving some inequalities, specifically, we generalize the Cauchy-Schwartz inequality.Sociedade Brasileira de Matemática Aplicada e Computacional2018-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300525TEMA (São Carlos) v.19 n.3 2018reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2018.019.03.0525info:eu-repo/semantics/openAccessSOUSA,J.V.C.OLIVEIRA,E.C.eng2018-12-13T00:00:00Zoai:scielo:S2179-84512018000300525Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2018-12-13T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Truncated ��-fractional Taylor’s Formula with Applications
title Truncated ��-fractional Taylor’s Formula with Applications
spellingShingle Truncated ��-fractional Taylor’s Formula with Applications
SOUSA,J.V.C.
Truncated �� -fractional derivative
multivariable truncated �� -fractional derivative
truncated �� -fractional partial derivative
truncated �� -fractional Jacobian matrix
truncated �� -fractional Green’s theorem
title_short Truncated ��-fractional Taylor’s Formula with Applications
title_full Truncated ��-fractional Taylor’s Formula with Applications
title_fullStr Truncated ��-fractional Taylor’s Formula with Applications
title_full_unstemmed Truncated ��-fractional Taylor’s Formula with Applications
title_sort Truncated ��-fractional Taylor’s Formula with Applications
author SOUSA,J.V.C.
author_facet SOUSA,J.V.C.
OLIVEIRA,E.C.
author_role author
author2 OLIVEIRA,E.C.
author2_role author
dc.contributor.author.fl_str_mv SOUSA,J.V.C.
OLIVEIRA,E.C.
dc.subject.por.fl_str_mv Truncated �� -fractional derivative
multivariable truncated �� -fractional derivative
truncated �� -fractional partial derivative
truncated �� -fractional Jacobian matrix
truncated �� -fractional Green’s theorem
topic Truncated �� -fractional derivative
multivariable truncated �� -fractional derivative
truncated �� -fractional partial derivative
truncated �� -fractional Jacobian matrix
truncated �� -fractional Green’s theorem
description ABSTRACT In this paper, we present and prove a new truncated �� -fractional Taylor’s formula using the truncated �� -fractional variation of constants formula. In this sense, we present the truncated �� -fractional Taylor’s remainder by means of �� -fractional integral, essential for analyzing and comparing the error, when approaching functions by polynomials. From these new results, some applications were made involving some inequalities, specifically, we generalize the Cauchy-Schwartz inequality.
publishDate 2018
dc.date.none.fl_str_mv 2018-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300525
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300525
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2018.019.03.0525
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.19 n.3 2018
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
instacron_str SBMAC
institution SBMAC
reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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