Time-fractional telegraph equation of distributed order in higher dimensions
Autor(a) principal: | |
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Data de Publicação: | 2021 |
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/10773/31781 |
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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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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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 |
format |
article |
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 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
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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1799137690811105280 |