Weighted generalized fractional integration by parts and the Euler-Lagrange equation
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/34273 |
Resumo: | Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted generalized fractional derivative in the Riemann–Liouville sense with its associated integral for the recently introduced weighted generalized fractional derivative with Mittag–Leffler kernel. We rewrite these operators equivalently in effective series, proving some interesting properties relating to the left and the right fractional operators. These results permit us to obtain the corresponding integration by parts formula. With the new general formula, we obtain an appropriate weighted Euler–Lagrange equation for dynamic optimization, extending those existing in the literature. We end with the application of an optimization variational problem to the quantum mechanics framework. |
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Weighted generalized fractional integration by parts and the Euler-Lagrange equationWeighted generalized fractional calculusIntegration by parts formulaEuler–Lagrange equationQuantum mechanicsCalculus of variationsIntegration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted generalized fractional derivative in the Riemann–Liouville sense with its associated integral for the recently introduced weighted generalized fractional derivative with Mittag–Leffler kernel. We rewrite these operators equivalently in effective series, proving some interesting properties relating to the left and the right fractional operators. These results permit us to obtain the corresponding integration by parts formula. With the new general formula, we obtain an appropriate weighted Euler–Lagrange equation for dynamic optimization, extending those existing in the literature. We end with the application of an optimization variational problem to the quantum mechanics framework.MDPI2022-07-25T14:28:07Z2022-04-15T00:00:00Z2022-04-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/34273eng10.3390/axioms11040178Zine, HoussineLotfi, El MehdiTorres, Delfim F. M.Yousfi, Nourainfo: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:RCAAP2024-02-22T12:04:50Zoai:ria.ua.pt:10773/34273Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:05:04.055656Repositório 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 |
Weighted generalized fractional integration by parts and the Euler-Lagrange equation |
title |
Weighted generalized fractional integration by parts and the Euler-Lagrange equation |
spellingShingle |
Weighted generalized fractional integration by parts and the Euler-Lagrange equation Zine, Houssine Weighted generalized fractional calculus Integration by parts formula Euler–Lagrange equation Quantum mechanics Calculus of variations |
title_short |
Weighted generalized fractional integration by parts and the Euler-Lagrange equation |
title_full |
Weighted generalized fractional integration by parts and the Euler-Lagrange equation |
title_fullStr |
Weighted generalized fractional integration by parts and the Euler-Lagrange equation |
title_full_unstemmed |
Weighted generalized fractional integration by parts and the Euler-Lagrange equation |
title_sort |
Weighted generalized fractional integration by parts and the Euler-Lagrange equation |
author |
Zine, Houssine |
author_facet |
Zine, Houssine Lotfi, El Mehdi Torres, Delfim F. M. Yousfi, Noura |
author_role |
author |
author2 |
Lotfi, El Mehdi Torres, Delfim F. M. Yousfi, Noura |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Zine, Houssine Lotfi, El Mehdi Torres, Delfim F. M. Yousfi, Noura |
dc.subject.por.fl_str_mv |
Weighted generalized fractional calculus Integration by parts formula Euler–Lagrange equation Quantum mechanics Calculus of variations |
topic |
Weighted generalized fractional calculus Integration by parts formula Euler–Lagrange equation Quantum mechanics Calculus of variations |
description |
Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted generalized fractional derivative in the Riemann–Liouville sense with its associated integral for the recently introduced weighted generalized fractional derivative with Mittag–Leffler kernel. We rewrite these operators equivalently in effective series, proving some interesting properties relating to the left and the right fractional operators. These results permit us to obtain the corresponding integration by parts formula. With the new general formula, we obtain an appropriate weighted Euler–Lagrange equation for dynamic optimization, extending those existing in the literature. We end with the application of an optimization variational problem to the quantum mechanics framework. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-07-25T14:28:07Z 2022-04-15T00:00:00Z 2022-04-15 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/34273 |
url |
http://hdl.handle.net/10773/34273 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.3390/axioms11040178 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
MDPI |
publisher.none.fl_str_mv |
MDPI |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799137705728147456 |