Optimizing variational problems through weighted fractional derivatives

Bibliographic Details
Main Author: Almeida, Ricardo
Publication Date: 2024
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/41996
Summary: In this article, we explore a variety of problems within the domain of calculus of variations, specifically in the context of fractional calculus. The fractional derivative we consider incorporates the notion of weighted fractional derivatives along with derivatives with respect to another function. Besides the fractional operators, the Lagrange function depends on extremal points. We examine the fundamental problem, providing the fractional Euler–Lagrange equation and the associated transversality conditions. Both the isoperimetric and Herglotz problems are also explored. Finally, we conclude with an analysis of the variational problem, incorporating fractional derivatives of any positive real order.
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spelling Optimizing variational problems through weighted fractional derivativesWeighted fractional derivativeFractional calculus of variationsEuler–Lagrange equationIn this article, we explore a variety of problems within the domain of calculus of variations, specifically in the context of fractional calculus. The fractional derivative we consider incorporates the notion of weighted fractional derivatives along with derivatives with respect to another function. Besides the fractional operators, the Lagrange function depends on extremal points. We examine the fundamental problem, providing the fractional Euler–Lagrange equation and the associated transversality conditions. Both the isoperimetric and Herglotz problems are also explored. Finally, we conclude with an analysis of the variational problem, incorporating fractional derivatives of any positive real order.MDPI2024-06-05T09:27:34Z2024-01-01T00:00:00Z2024info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/41996eng10.3390/fractalfract8050272Almeida, Ricardoinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-06-10T01:47:34Zoai:ria.ua.pt:10773/41996Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T17:55:13.248213Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Optimizing variational problems through weighted fractional derivatives
title Optimizing variational problems through weighted fractional derivatives
spellingShingle Optimizing variational problems through weighted fractional derivatives
Almeida, Ricardo
Weighted fractional derivative
Fractional calculus of variations
Euler–Lagrange equation
title_short Optimizing variational problems through weighted fractional derivatives
title_full Optimizing variational problems through weighted fractional derivatives
title_fullStr Optimizing variational problems through weighted fractional derivatives
title_full_unstemmed Optimizing variational problems through weighted fractional derivatives
title_sort Optimizing variational problems through weighted fractional derivatives
author Almeida, Ricardo
author_facet Almeida, Ricardo
author_role author
dc.contributor.author.fl_str_mv Almeida, Ricardo
dc.subject.por.fl_str_mv Weighted fractional derivative
Fractional calculus of variations
Euler–Lagrange equation
topic Weighted fractional derivative
Fractional calculus of variations
Euler–Lagrange equation
description In this article, we explore a variety of problems within the domain of calculus of variations, specifically in the context of fractional calculus. The fractional derivative we consider incorporates the notion of weighted fractional derivatives along with derivatives with respect to another function. Besides the fractional operators, the Lagrange function depends on extremal points. We examine the fundamental problem, providing the fractional Euler–Lagrange equation and the associated transversality conditions. Both the isoperimetric and Herglotz problems are also explored. Finally, we conclude with an analysis of the variational problem, incorporating fractional derivatives of any positive real order.
publishDate 2024
dc.date.none.fl_str_mv 2024-06-05T09:27:34Z
2024-01-01T00:00:00Z
2024
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/10773/41996
url http://hdl.handle.net/10773/41996
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.3390/fractalfract8050272
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
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repository.mail.fl_str_mv info@rcaap.pt
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