A stochastic fractional calculus with applications to variational principles

Detalhes bibliográficos
Autor(a) principal: Zine, Houssine
Data de Publicação: 2020
Outros Autores: Torres, Delfim F. M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/28984
Resumo: We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional Euler-Lagrange equation is obtained, extending those available in the literature for the classical, fractional, and stochastic calculus of variations. To illustrate our main theoretical result, we discuss two examples: one derived from quantum mechanics, the second validated by an adequate numerical simulation.
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spelling A stochastic fractional calculus with applications to variational principlesFractional derivatives and integralsStochastic processesCalculus of variationsWe introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional Euler-Lagrange equation is obtained, extending those available in the literature for the classical, fractional, and stochastic calculus of variations. To illustrate our main theoretical result, we discuss two examples: one derived from quantum mechanics, the second validated by an adequate numerical simulation.MDPI2020-08-04T09:01:25Z2020-09-01T00:00:00Z2020-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/28984eng10.3390/fractalfract4030038Zine, HoussineTorres, Delfim F. M.info: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:RCAAP2024-02-22T11:56:03Zoai:ria.ua.pt:10773/28984Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:01:25.984474Repositório 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 A stochastic fractional calculus with applications to variational principles
title A stochastic fractional calculus with applications to variational principles
spellingShingle A stochastic fractional calculus with applications to variational principles
Zine, Houssine
Fractional derivatives and integrals
Stochastic processes
Calculus of variations
title_short A stochastic fractional calculus with applications to variational principles
title_full A stochastic fractional calculus with applications to variational principles
title_fullStr A stochastic fractional calculus with applications to variational principles
title_full_unstemmed A stochastic fractional calculus with applications to variational principles
title_sort A stochastic fractional calculus with applications to variational principles
author Zine, Houssine
author_facet Zine, Houssine
Torres, Delfim F. M.
author_role author
author2 Torres, Delfim F. M.
author2_role author
dc.contributor.author.fl_str_mv Zine, Houssine
Torres, Delfim F. M.
dc.subject.por.fl_str_mv Fractional derivatives and integrals
Stochastic processes
Calculus of variations
topic Fractional derivatives and integrals
Stochastic processes
Calculus of variations
description We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional Euler-Lagrange equation is obtained, extending those available in the literature for the classical, fractional, and stochastic calculus of variations. To illustrate our main theoretical result, we discuss two examples: one derived from quantum mechanics, the second validated by an adequate numerical simulation.
publishDate 2020
dc.date.none.fl_str_mv 2020-08-04T09:01:25Z
2020-09-01T00:00:00Z
2020-09
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/28984
url http://hdl.handle.net/10773/28984
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.3390/fractalfract4030038
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eu_rights_str_mv openAccess
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