Time-fractional telegraph equation of distributed order in higher dimensions

Detalhes bibliográficos
Autor(a) principal: Vieira, N.
Data de Publicação: 2021
Outros Autores: Rodrigues, M. M., Ferreira, 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/10773/31781
Resumo: In this work, the Cauchy problem for the time-fractional telegraph equation of distributed order in $\BR^n \times \BR^+$ 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 transformFourier transformMellin transformFox H-functionsFractional momentsTauberian TheoremIn this work, the Cauchy problem for the time-fractional telegraph equation of distributed order in $\BR^n \times \BR^+$ 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.Elsevier2021-112021-11-01T00:00:00Z2023-10-31T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/31781eng1007-570410.1016/j.cnsns.2021.105925Vieira, N.Rodrigues, M. M.Ferreira, M.info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:01:14Zoai:ria.ua.pt:10773/31781Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:03:32.675889Repositório 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, N.
Time-fractional telegraph equation
Distributed order
Laplace transform
Fourier transform
Mellin transform
Fox H-functions
Fractional moments
Tauberian Theorem
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, N.
author_facet Vieira, N.
Rodrigues, M. M.
Ferreira, M.
author_role author
author2 Rodrigues, M. M.
Ferreira, M.
author2_role author
author
dc.contributor.author.fl_str_mv Vieira, N.
Rodrigues, M. M.
Ferreira, M.
dc.subject.por.fl_str_mv Time-fractional telegraph equation
Distributed order
Laplace transform
Fourier transform
Mellin transform
Fox H-functions
Fractional moments
Tauberian Theorem
topic Time-fractional telegraph equation
Distributed order
Laplace transform
Fourier transform
Mellin transform
Fox H-functions
Fractional moments
Tauberian Theorem
description In this work, the Cauchy problem for the time-fractional telegraph equation of distributed order in $\BR^n \times \BR^+$ 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
2023-10-31T00:00:00Z
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/10773/31781
url http://hdl.handle.net/10773/31781
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1007-5704
10.1016/j.cnsns.2021.105925
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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)
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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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