First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators

Detalhes bibliográficos
Autor(a) principal: Ferreira, Milton
Data de Publicação: 2018
Outros Autores: Rodrigues, Manuela, Vieira, Nelson Felipe Loureiro
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/23631
Resumo: In this work, we obtain the first and second fundamental solutions (FS) of the multidimensional time-fractional equation with Laplace or Dirac operators, where the two time-fractional derivatives of orders α ∈]0, 1] and β ∈]1, 2] are in the Caputo sense. We obtain representations of the FS in terms of Hankel transform, double Mellin- Barnes integrals, and H-functions of two variables. As an application, the FS are used to solve Cauchy problems of Laplace and Dirac type.
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spelling First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operatorsTime-fractional telegraph equationTime-fractional telegraph Dirac operatorFirst and second fundamental solutionsCaputo fractional derivativeMultivariate Mittag-Leffler functionH-function of two variablesIn this work, we obtain the first and second fundamental solutions (FS) of the multidimensional time-fractional equation with Laplace or Dirac operators, where the two time-fractional derivatives of orders α ∈]0, 1] and β ∈]1, 2] are in the Caputo sense. We obtain representations of the FS in terms of Hankel transform, double Mellin- Barnes integrals, and H-functions of two variables. As an application, the FS are used to solve Cauchy problems of Laplace and Dirac type.Springer2018-052018-05-01T00:00:00Z2019-05-01T11:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/23631eng0188-700910.1007/s00006-018-0858-7Ferreira, MiltonRodrigues, ManuelaVieira, Nelson Felipe Loureiroinfo: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:RCAAP2024-02-22T11:45:04Zoai:ria.ua.pt:10773/23631Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:57:00.390199Repositório 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 First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators
title First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators
spellingShingle First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators
Ferreira, Milton
Time-fractional telegraph equation
Time-fractional telegraph Dirac operator
First and second fundamental solutions
Caputo fractional derivative
Multivariate Mittag-Leffler function
H-function of two variables
title_short First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators
title_full First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators
title_fullStr First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators
title_full_unstemmed First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators
title_sort First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators
author Ferreira, Milton
author_facet Ferreira, Milton
Rodrigues, Manuela
Vieira, Nelson Felipe Loureiro
author_role author
author2 Rodrigues, Manuela
Vieira, Nelson Felipe Loureiro
author2_role author
author
dc.contributor.author.fl_str_mv Ferreira, Milton
Rodrigues, Manuela
Vieira, Nelson Felipe Loureiro
dc.subject.por.fl_str_mv Time-fractional telegraph equation
Time-fractional telegraph Dirac operator
First and second fundamental solutions
Caputo fractional derivative
Multivariate Mittag-Leffler function
H-function of two variables
topic Time-fractional telegraph equation
Time-fractional telegraph Dirac operator
First and second fundamental solutions
Caputo fractional derivative
Multivariate Mittag-Leffler function
H-function of two variables
description In this work, we obtain the first and second fundamental solutions (FS) of the multidimensional time-fractional equation with Laplace or Dirac operators, where the two time-fractional derivatives of orders α ∈]0, 1] and β ∈]1, 2] are in the Caputo sense. We obtain representations of the FS in terms of Hankel transform, double Mellin- Barnes integrals, and H-functions of two variables. As an application, the FS are used to solve Cauchy problems of Laplace and Dirac type.
publishDate 2018
dc.date.none.fl_str_mv 2018-05
2018-05-01T00:00:00Z
2019-05-01T11:00:00Z
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/10773/23631
url http://hdl.handle.net/10773/23631
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0188-7009
10.1007/s00006-018-0858-7
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: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
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