Time-fractional telegraph equation of distributed order in higher dimensions

Detalhes bibliográficos
Autor(a) principal: Vieira, Nelson
Data de Publicação: 2021
Outros Autores: Rodrigues, M. Manuela, Ferreira, Milton
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.8/7512
Resumo: In this work, the Cauchy problem for the time-fractional telegraph equation of distributed order in Rn is considered. By employing the technique of the Fourier, Laplace, and Mellin transforms, a representation of the fundamental solution of this equation in terms of convolutions involving the Fox H-function is obtained. Some particular choices of the density functions in the form of elementary functions are studied. Fractional moments of the fundamental solution are computed in the Laplace domain. Finally, by application of the Tauberian theorems we study the asymptotic behaviour of the second-order moment (variance) in the time domain.
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spelling Time-fractional telegraph equation of distributed order in higher dimensionsTime-fractional telegraph equationDistributed orderLaplace, Fourier and Mellin transformsFox H-functionsFractional momentsTauberian theoremsIn this work, the Cauchy problem for the time-fractional telegraph equation of distributed order in Rn is considered. By employing the technique of the Fourier, Laplace, and Mellin transforms, a representation of the fundamental solution of this equation in terms of convolutions involving the Fox H-function is obtained. Some particular choices of the density functions in the form of elementary functions are studied. Fractional moments of the fundamental solution are computed in the Laplace domain. Finally, by application of the Tauberian theorems we study the asymptotic behaviour of the second-order moment (variance) in the time domain.ElsevierIC-OnlineVieira, NelsonRodrigues, M. ManuelaFerreira, Milton2023-11-04T01:30:19Z2021-112021-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/7512engN. Vieira, M.M. Rodrigues, and M. Ferreira, Time-fractional telegraph equation of distributed order in higher dimensions, Commun. Nonlinear Sci. Numer. Simul., Vol. 102, 2021, Page: 10592510.1016/j.cnsns.2021.105925info: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:RCAAP2024-01-17T15:55:19Zoai:iconline.ipleiria.pt:10400.8/7512Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:50:27.270550Repositório 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 Time-fractional telegraph equation of distributed order in higher dimensions
title Time-fractional telegraph equation of distributed order in higher dimensions
spellingShingle Time-fractional telegraph equation of distributed order in higher dimensions
Vieira, Nelson
Time-fractional telegraph equation
Distributed order
Laplace, Fourier and Mellin transforms
Fox H-functions
Fractional moments
Tauberian theorems
title_short Time-fractional telegraph equation of distributed order in higher dimensions
title_full Time-fractional telegraph equation of distributed order in higher dimensions
title_fullStr Time-fractional telegraph equation of distributed order in higher dimensions
title_full_unstemmed Time-fractional telegraph equation of distributed order in higher dimensions
title_sort Time-fractional telegraph equation of distributed order in higher dimensions
author Vieira, Nelson
author_facet Vieira, Nelson
Rodrigues, M. Manuela
Ferreira, Milton
author_role author
author2 Rodrigues, M. Manuela
Ferreira, Milton
author2_role author
author
dc.contributor.none.fl_str_mv IC-Online
dc.contributor.author.fl_str_mv Vieira, Nelson
Rodrigues, M. Manuela
Ferreira, Milton
dc.subject.por.fl_str_mv Time-fractional telegraph equation
Distributed order
Laplace, Fourier and Mellin transforms
Fox H-functions
Fractional moments
Tauberian theorems
topic Time-fractional telegraph equation
Distributed order
Laplace, Fourier and Mellin transforms
Fox H-functions
Fractional moments
Tauberian theorems
description In this work, the Cauchy problem for the time-fractional telegraph equation of distributed order in Rn is considered. By employing the technique of the Fourier, Laplace, and Mellin transforms, a representation of the fundamental solution of this equation in terms of convolutions involving the Fox H-function is obtained. Some particular choices of the density functions in the form of elementary functions are studied. Fractional moments of the fundamental solution are computed in the Laplace domain. Finally, by application of the Tauberian theorems we study the asymptotic behaviour of the second-order moment (variance) in the time domain.
publishDate 2021
dc.date.none.fl_str_mv 2021-11
2021-11-01T00:00:00Z
2023-11-04T01:30:19Z
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/10400.8/7512
url http://hdl.handle.net/10400.8/7512
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv N. Vieira, M.M. Rodrigues, and M. Ferreira, Time-fractional telegraph equation of distributed order in higher dimensions, Commun. Nonlinear Sci. Numer. Simul., Vol. 102, 2021, Page: 105925
10.1016/j.cnsns.2021.105925
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 Elsevier
publisher.none.fl_str_mv Elsevier
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
repository.mail.fl_str_mv
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