Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

Detalhes bibliográficos
Autor(a) principal: Ferreira, Milton dos Santos
Data de Publicação: 2016
Outros Autores: Vieira, Nelson Felipe Loureiro
Idioma: eng
Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Texto Completo: http://hdl.handle.net/10773/16008
Resumo: In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.
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spelling Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operatorsFractional partial differential equationsFractional Laplace and Dirac operatorsCaputo derivativeEigenfunctionsFundamental solutionIn this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.Springer2018-07-20T14:00:55Z2016-01-01T00:00:00Z20162016-12-31T11:00:00Zbook partinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10773/16008eng978-3-319-42528-3Ferreira, Milton dos SantosVieira, Nelson Felipe Loureiroinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T03:57:40Zoai:ria.ua.pt:10773/16008Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:52:33.289860Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators
title Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators
spellingShingle Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators
Ferreira, Milton dos Santos
Fractional partial differential equations
Fractional Laplace and Dirac operators
Caputo derivative
Eigenfunctions
Fundamental solution
title_short Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators
title_full Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators
title_fullStr Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators
title_full_unstemmed Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators
title_sort Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators
author Ferreira, Milton dos Santos
author_facet Ferreira, Milton dos Santos
Vieira, Nelson Felipe Loureiro
author_role author
author2 Vieira, Nelson Felipe Loureiro
author2_role author
dc.contributor.author.fl_str_mv Ferreira, Milton dos Santos
Vieira, Nelson Felipe Loureiro
dc.subject.por.fl_str_mv Fractional partial differential equations
Fractional Laplace and Dirac operators
Caputo derivative
Eigenfunctions
Fundamental solution
topic Fractional partial differential equations
Fractional Laplace and Dirac operators
Caputo derivative
Eigenfunctions
Fundamental solution
description In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.
publishDate 2016
dc.date.none.fl_str_mv 2016-01-01T00:00:00Z
2016
2016-12-31T11:00:00Z
2018-07-20T14:00:55Z
dc.type.driver.fl_str_mv book part
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/16008
url http://hdl.handle.net/10773/16008
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 978-3-319-42528-3
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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