Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators

Detalhes bibliográficos
Autor(a) principal: Ferreira, Milton
Data de Publicação: 2017
Outros Autores: 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/10400.8/3824
Resumo: In this paper we study the multidimensional time fractional diffusion-wave equation where the time fractional derivative is in the Caputo sense with order . Applying operational techniques via Fourier and Mellin transforms we obtain an integral representation of the fundamental solution (FS) of the time fractional diffusion-wave operator. Series representations of the FS are explicitly obtained for any dimension. From these we derive the FS for the time fractional parabolic Dirac operator in the form of integral and series representation. Fractional moments of arbitrary order are also computed. To illustrate our results we present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameter.
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spelling Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operatorsTime fractional diffusion-wave operatorTime fractional parabolic Dirac operatorFundamental solutionsCaputo fractional derivativeFractional momentsIn this paper we study the multidimensional time fractional diffusion-wave equation where the time fractional derivative is in the Caputo sense with order . Applying operational techniques via Fourier and Mellin transforms we obtain an integral representation of the fundamental solution (FS) of the time fractional diffusion-wave operator. Series representations of the FS are explicitly obtained for any dimension. From these we derive the FS for the time fractional parabolic Dirac operator in the form of integral and series representation. Fractional moments of arbitrary order are also computed. To illustrate our results we present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameter.ElsevierIC-OnlineFerreira, MiltonVieira, Nelson Felipe Loureiro2019-02-07T16:40:38Z2017-03-012017-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/3824engFerreira, M., and Vieira, N. Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators, J. Math. Anal. Appl., 447(1), 2017, 329-353.0022-247X10.1016/j.jmaa.2016.08.052info: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:RCAAP2024-01-17T15:47:59Zoai:iconline.ipleiria.pt:10400.8/3824Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:47:50.766285Repositório 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 Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
title Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
spellingShingle Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
Ferreira, Milton
Time fractional diffusion-wave operator
Time fractional parabolic Dirac operator
Fundamental solutions
Caputo fractional derivative
Fractional moments
title_short Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
title_full Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
title_fullStr Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
title_full_unstemmed Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
title_sort Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
author Ferreira, Milton
author_facet Ferreira, Milton
Vieira, Nelson Felipe Loureiro
author_role author
author2 Vieira, Nelson Felipe Loureiro
author2_role author
dc.contributor.none.fl_str_mv IC-Online
dc.contributor.author.fl_str_mv Ferreira, Milton
Vieira, Nelson Felipe Loureiro
dc.subject.por.fl_str_mv Time fractional diffusion-wave operator
Time fractional parabolic Dirac operator
Fundamental solutions
Caputo fractional derivative
Fractional moments
topic Time fractional diffusion-wave operator
Time fractional parabolic Dirac operator
Fundamental solutions
Caputo fractional derivative
Fractional moments
description In this paper we study the multidimensional time fractional diffusion-wave equation where the time fractional derivative is in the Caputo sense with order . Applying operational techniques via Fourier and Mellin transforms we obtain an integral representation of the fundamental solution (FS) of the time fractional diffusion-wave operator. Series representations of the FS are explicitly obtained for any dimension. From these we derive the FS for the time fractional parabolic Dirac operator in the form of integral and series representation. Fractional moments of arbitrary order are also computed. To illustrate our results we present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameter.
publishDate 2017
dc.date.none.fl_str_mv 2017-03-01
2017-03-01T00:00:00Z
2019-02-07T16:40:38Z
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/10400.8/3824
url http://hdl.handle.net/10400.8/3824
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Ferreira, M., and Vieira, N. Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators, J. Math. Anal. Appl., 447(1), 2017, 329-353.
0022-247X
10.1016/j.jmaa.2016.08.052
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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