A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative

Bibliographic Details
Main Author: Almeida, Ricardo
Publication Date: 2019
Other Authors: Jleli, Mohamed, Samet, Bessem
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/26178
Summary: We provide a numerical method to solve a certain class of fractional differential equations involving ψ -Caputo fractional derivative. The considered class includes as particular case fractional relaxation–oscillation equations. Our approach is based on operational matrix of fractional integration of a new type of orthogonal polynomials. More precisely, we introduce ψ -shifted Legendre polynomial basis, and we derive an explicit formula for the ψ -fractional integral of ψ -shifted Legendre polynomials. Next, via an orthogonal projection on this polynomial basis, the problem is reduced to an algebraic equation that can be easily solved. The convergence of the method is justified rigorously and confirmed by some numerical experiments.
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spelling A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivativeψ -Shiftedψ -Caputo fractional derivativeFractional relaxation–oscillation equationConvergenceWe provide a numerical method to solve a certain class of fractional differential equations involving ψ -Caputo fractional derivative. The considered class includes as particular case fractional relaxation–oscillation equations. Our approach is based on operational matrix of fractional integration of a new type of orthogonal polynomials. More precisely, we introduce ψ -shifted Legendre polynomial basis, and we derive an explicit formula for the ψ -fractional integral of ψ -shifted Legendre polynomials. Next, via an orthogonal projection on this polynomial basis, the problem is reduced to an algebraic equation that can be easily solved. The convergence of the method is justified rigorously and confirmed by some numerical experiments.Springer2020-07-01T00:00:00Z2019-07-01T00:00:00Z2019-07info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/26178eng1578-730310.1007/s13398-018-0590-0Almeida, RicardoJleli, MohamedSamet, Besseminfo: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:RCAAP2024-05-06T04:20:43Zoai:ria.ua.pt:10773/26178Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:05:21.083092Repositórios 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 A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative
title A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative
spellingShingle A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative
Almeida, Ricardo
ψ -Shifted
ψ -Caputo fractional derivative
Fractional relaxation–oscillation equation
Convergence
title_short A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative
title_full A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative
title_fullStr A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative
title_full_unstemmed A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative
title_sort A numerical study of fractional relaxation–oscillation equations involving ψ-Caputo fractional derivative
author Almeida, Ricardo
author_facet Almeida, Ricardo
Jleli, Mohamed
Samet, Bessem
author_role author
author2 Jleli, Mohamed
Samet, Bessem
author2_role author
author
dc.contributor.author.fl_str_mv Almeida, Ricardo
Jleli, Mohamed
Samet, Bessem
dc.subject.por.fl_str_mv ψ -Shifted
ψ -Caputo fractional derivative
Fractional relaxation–oscillation equation
Convergence
topic ψ -Shifted
ψ -Caputo fractional derivative
Fractional relaxation–oscillation equation
Convergence
description We provide a numerical method to solve a certain class of fractional differential equations involving ψ -Caputo fractional derivative. The considered class includes as particular case fractional relaxation–oscillation equations. Our approach is based on operational matrix of fractional integration of a new type of orthogonal polynomials. More precisely, we introduce ψ -shifted Legendre polynomial basis, and we derive an explicit formula for the ψ -fractional integral of ψ -shifted Legendre polynomials. Next, via an orthogonal projection on this polynomial basis, the problem is reduced to an algebraic equation that can be easily solved. The convergence of the method is justified rigorously and confirmed by some numerical experiments.
publishDate 2019
dc.date.none.fl_str_mv 2019-07-01T00:00:00Z
2019-07
2020-07-01T00:00:00Z
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/10773/26178
url http://hdl.handle.net/10773/26178
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1578-7303
10.1007/s13398-018-0590-0
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 Springer
publisher.none.fl_str_mv Springer
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
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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