A prelude to the fractional calculus applied to tumor dynamic

Detalhes bibliográficos
Autor(a) principal: Varalta,N.
Data de Publicação: 2014
Outros Autores: Gomes,A.V., Camargo,R.F.
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=S2179-84512014000200008
Resumo: In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i.e., we replace the ordinary derivative of order 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 1, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.
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spelling A prelude to the fractional calculus applied to tumor dynamicbiomathematicsfractional calculuslogistics equationdynamics of cancer tumorIn order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i.e., we replace the ordinary derivative of order 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 1, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.Sociedade Brasileira de Matemática Aplicada e Computacional2014-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512014000200008TEMA (São Carlos) v.15 n.2 2014reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2014.015.02.0211info:eu-repo/semantics/openAccessVaralta,N.Gomes,A.V.Camargo,R.F.eng2014-09-10T00:00:00Zoai:scielo:S2179-84512014000200008Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2014-09-10T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv A prelude to the fractional calculus applied to tumor dynamic
title A prelude to the fractional calculus applied to tumor dynamic
spellingShingle A prelude to the fractional calculus applied to tumor dynamic
Varalta,N.
biomathematics
fractional calculus
logistics equation
dynamics of cancer tumor
title_short A prelude to the fractional calculus applied to tumor dynamic
title_full A prelude to the fractional calculus applied to tumor dynamic
title_fullStr A prelude to the fractional calculus applied to tumor dynamic
title_full_unstemmed A prelude to the fractional calculus applied to tumor dynamic
title_sort A prelude to the fractional calculus applied to tumor dynamic
author Varalta,N.
author_facet Varalta,N.
Gomes,A.V.
Camargo,R.F.
author_role author
author2 Gomes,A.V.
Camargo,R.F.
author2_role author
author
dc.contributor.author.fl_str_mv Varalta,N.
Gomes,A.V.
Camargo,R.F.
dc.subject.por.fl_str_mv biomathematics
fractional calculus
logistics equation
dynamics of cancer tumor
topic biomathematics
fractional calculus
logistics equation
dynamics of cancer tumor
description In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i.e., we replace the ordinary derivative of order 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 1, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.
publishDate 2014
dc.date.none.fl_str_mv 2014-08-01
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=S2179-84512014000200008
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512014000200008
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2014.015.02.0211
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.15 n.2 2014
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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