Fractional order calculus: historical apologia, basic concepts and some applications
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Revista Brasileira de Ensino de Física (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172011000400002 |
Resumo: | Fractional order calculus (FOC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus. However, until recently, it has been investigated mainly from a mathematical point of view. Advances in the field of fractals have revealed its subtle relationships with fractional calculus. Nonetheless, fractional calculus is generally excluded from standard courses in mathematics, partly because many mathematicians are unfamiliar with its nature and its applications. This area has emerged as a useful tool among researchers. One of the objectives of this paper is to discuss the usefulness of fractional calculus in applied sciences and engineering. In view of the increasing interest in the development of the new paradigm, another objective is to encourage the use of this mathematical idea in various scientific areas by means of a historical apologia for the development of fractional calculus. |
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Fractional order calculus: historical apologia, basic concepts and some applicationsfractional order calculusnon-integer order systemsdynamical systemsFractional order calculus (FOC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus. However, until recently, it has been investigated mainly from a mathematical point of view. Advances in the field of fractals have revealed its subtle relationships with fractional calculus. Nonetheless, fractional calculus is generally excluded from standard courses in mathematics, partly because many mathematicians are unfamiliar with its nature and its applications. This area has emerged as a useful tool among researchers. One of the objectives of this paper is to discuss the usefulness of fractional calculus in applied sciences and engineering. In view of the increasing interest in the development of the new paradigm, another objective is to encourage the use of this mathematical idea in various scientific areas by means of a historical apologia for the development of fractional calculus.Sociedade Brasileira de Física2011-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172011000400002Revista Brasileira de Ensino de Física v.33 n.4 2011reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S1806-11172011000400002info:eu-repo/semantics/openAccessDavid,S.A.Linares,J.L.Pallone,E.M.J.A.eng2012-03-02T00:00:00Zoai:scielo:S1806-11172011000400002Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2012-03-02T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false |
dc.title.none.fl_str_mv |
Fractional order calculus: historical apologia, basic concepts and some applications |
title |
Fractional order calculus: historical apologia, basic concepts and some applications |
spellingShingle |
Fractional order calculus: historical apologia, basic concepts and some applications David,S.A. fractional order calculus non-integer order systems dynamical systems |
title_short |
Fractional order calculus: historical apologia, basic concepts and some applications |
title_full |
Fractional order calculus: historical apologia, basic concepts and some applications |
title_fullStr |
Fractional order calculus: historical apologia, basic concepts and some applications |
title_full_unstemmed |
Fractional order calculus: historical apologia, basic concepts and some applications |
title_sort |
Fractional order calculus: historical apologia, basic concepts and some applications |
author |
David,S.A. |
author_facet |
David,S.A. Linares,J.L. Pallone,E.M.J.A. |
author_role |
author |
author2 |
Linares,J.L. Pallone,E.M.J.A. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
David,S.A. Linares,J.L. Pallone,E.M.J.A. |
dc.subject.por.fl_str_mv |
fractional order calculus non-integer order systems dynamical systems |
topic |
fractional order calculus non-integer order systems dynamical systems |
description |
Fractional order calculus (FOC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus. However, until recently, it has been investigated mainly from a mathematical point of view. Advances in the field of fractals have revealed its subtle relationships with fractional calculus. Nonetheless, fractional calculus is generally excluded from standard courses in mathematics, partly because many mathematicians are unfamiliar with its nature and its applications. This area has emerged as a useful tool among researchers. One of the objectives of this paper is to discuss the usefulness of fractional calculus in applied sciences and engineering. In view of the increasing interest in the development of the new paradigm, another objective is to encourage the use of this mathematical idea in various scientific areas by means of a historical apologia for the development of fractional calculus. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-12-01 |
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=S1806-11172011000400002 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172011000400002 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1806-11172011000400002 |
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 Física |
publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
dc.source.none.fl_str_mv |
Revista Brasileira de Ensino de Física v.33 n.4 2011 reponame:Revista Brasileira de Ensino de Física (Online) instname:Sociedade Brasileira de Física (SBF) instacron:SBF |
instname_str |
Sociedade Brasileira de Física (SBF) |
instacron_str |
SBF |
institution |
SBF |
reponame_str |
Revista Brasileira de Ensino de Física (Online) |
collection |
Revista Brasileira de Ensino de Física (Online) |
repository.name.fl_str_mv |
Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF) |
repository.mail.fl_str_mv |
||marcio@sbfisica.org.br |
_version_ |
1752122421392965632 |