First and second fundamental solutions of the time-fractional telegraph equation of order 2α
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2018 |
| 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/10773/25339 |
Resumo: | In this work we obtain the first and second fundamental solutions of the multidimensional time-fractional equation of order $2\alpha$, $\alpha \in ]0,1]$, where the two time-fractional derivatives are in the Caputo sense. We obtain representations of the fundamental solutions in terms of Hankel transform, double Mellin-Barnes integral, and H-functions of two variables. As an application, the fundamental solutions are used to solve a Cauchy problem, and to study telegraph process with Brownian time. |
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First and second fundamental solutions of the time-fractional telegraph equation of order 2αTime-fractional telegraph equationTelegraph 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 of the multidimensional time-fractional equation of order $2\alpha$, $\alpha \in ]0,1]$, where the two time-fractional derivatives are in the Caputo sense. We obtain representations of the fundamental solutions in terms of Hankel transform, double Mellin-Barnes integral, and H-functions of two variables. As an application, the fundamental solutions are used to solve a Cauchy problem, and to study telegraph process with Brownian time.AIP Publishing2020-02-06T00:00:00Z2018-01-01T00:00:00Z2018info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/25339eng978-0-7354-1772-410.1063/1.5081599Ferreira, Milton dos SantosRodrigues, Maria Manuela FernandesVieira, Nelson Felipeinfo: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:RCAAP2024-02-22T11:49:08Zoai:ria.ua.pt:10773/25339Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:58:36.425086Repositório 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 of order 2α |
| title |
First and second fundamental solutions of the time-fractional telegraph equation of order 2α |
| spellingShingle |
First and second fundamental solutions of the time-fractional telegraph equation of order 2α Ferreira, Milton dos Santos Time-fractional telegraph equation 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 of order 2α |
| title_full |
First and second fundamental solutions of the time-fractional telegraph equation of order 2α |
| title_fullStr |
First and second fundamental solutions of the time-fractional telegraph equation of order 2α |
| title_full_unstemmed |
First and second fundamental solutions of the time-fractional telegraph equation of order 2α |
| title_sort |
First and second fundamental solutions of the time-fractional telegraph equation of order 2α |
| author |
Ferreira, Milton dos Santos |
| author_facet |
Ferreira, Milton dos Santos Rodrigues, Maria Manuela Fernandes Vieira, Nelson Felipe |
| author_role |
author |
| author2 |
Rodrigues, Maria Manuela Fernandes Vieira, Nelson Felipe |
| author2_role |
author author |
| dc.contributor.author.fl_str_mv |
Ferreira, Milton dos Santos Rodrigues, Maria Manuela Fernandes Vieira, Nelson Felipe |
| dc.subject.por.fl_str_mv |
Time-fractional telegraph equation 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 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 of the multidimensional time-fractional equation of order $2\alpha$, $\alpha \in ]0,1]$, where the two time-fractional derivatives are in the Caputo sense. We obtain representations of the fundamental solutions in terms of Hankel transform, double Mellin-Barnes integral, and H-functions of two variables. As an application, the fundamental solutions are used to solve a Cauchy problem, and to study telegraph process with Brownian time. |
| publishDate |
2018 |
| dc.date.none.fl_str_mv |
2018-01-01T00:00:00Z 2018 2020-02-06T00:00:00Z |
| 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/10773/25339 |
| url |
http://hdl.handle.net/10773/25339 |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
978-0-7354-1772-4 10.1063/1.5081599 |
| 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 |
AIP Publishing |
| publisher.none.fl_str_mv |
AIP Publishing |
| 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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
| institution |
RCAAP |
| reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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