Eigenfunctions of the time‐fractional diffusion‐wave operator
Autor(a) principal: | |
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Data de Publicação: | 2020 |
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/10400.8/5523 |
Resumo: | In this paper, we present some new integral and series representations for the eigenfunctions of the multidimensional time-fractional diffusion-wave operator with the time-fractional derivative of order $\beta \in ]1,2[$ defined in the Caputo sense. The integral representations are obtained in form of the inverse Fourier-Bessel transform and as double contour integrals of the Mellin-Barnes type. Concerning series expansions, the eigenfunctions are expressed as the double generalized hypergeometric series for any $\beta \in ]1,2[$ and as Kamp\'{e} de F\'{e}riet and Lauricella series in two variables for the rational values of $\beta$. The limit cases $\beta=1$ (diffusion operator) and $\beta=2$ (wave operator) as well as an intermediate case $\beta=\frac{3}{2}$ are studied in detail. Finally, we provide several plots of the eigenfunctions to some selected eigenvalues for different particular values of the fractional derivative order $\beta$ and the spatial dimension $n$. |
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Eigenfunctions of the time‐fractional diffusion‐wave operatorTime-fractional diffusion-wave operator Eigenfunctions; Caputo fractional derivatives; Generalized hypergeometric series.EigenfunctionsCaputo fractional derivativesGeneralized hypergeometric seriesIn this paper, we present some new integral and series representations for the eigenfunctions of the multidimensional time-fractional diffusion-wave operator with the time-fractional derivative of order $\beta \in ]1,2[$ defined in the Caputo sense. The integral representations are obtained in form of the inverse Fourier-Bessel transform and as double contour integrals of the Mellin-Barnes type. Concerning series expansions, the eigenfunctions are expressed as the double generalized hypergeometric series for any $\beta \in ]1,2[$ and as Kamp\'{e} de F\'{e}riet and Lauricella series in two variables for the rational values of $\beta$. The limit cases $\beta=1$ (diffusion operator) and $\beta=2$ (wave operator) as well as an intermediate case $\beta=\frac{3}{2}$ are studied in detail. Finally, we provide several plots of the eigenfunctions to some selected eigenvalues for different particular values of the fractional derivative order $\beta$ and the spatial dimension $n$.Wiley Online LibraryIC-OnlineFerreira, M.Luchko, Yu.Rodrigues, M. M.Vieira, N.2021-12-01T01:30:15Z2020-12-062020-12-06T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/5523engFerreira, M., Luchko, Yu., Rodrigues, M.M., Vieira, N., Eigenfunctions of the time‐fractional diffusion‐wave operator. Math Meth Appl Sci. 2021; 44(2): 1713–1743. https://doi.org/10.1002/mma.68740170-4214https://doi.org/10.1002/mma.6874info: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:RCAAP2024-01-17T15:51:18Zoai:iconline.ipleiria.pt:10400.8/5523Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:49:01.145564Repositório 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 |
Eigenfunctions of the time‐fractional diffusion‐wave operator |
title |
Eigenfunctions of the time‐fractional diffusion‐wave operator |
spellingShingle |
Eigenfunctions of the time‐fractional diffusion‐wave operator Ferreira, M. Time-fractional diffusion-wave operator Eigenfunctions; Caputo fractional derivatives; Generalized hypergeometric series. Eigenfunctions Caputo fractional derivatives Generalized hypergeometric series |
title_short |
Eigenfunctions of the time‐fractional diffusion‐wave operator |
title_full |
Eigenfunctions of the time‐fractional diffusion‐wave operator |
title_fullStr |
Eigenfunctions of the time‐fractional diffusion‐wave operator |
title_full_unstemmed |
Eigenfunctions of the time‐fractional diffusion‐wave operator |
title_sort |
Eigenfunctions of the time‐fractional diffusion‐wave operator |
author |
Ferreira, M. |
author_facet |
Ferreira, M. Luchko, Yu. Rodrigues, M. M. Vieira, N. |
author_role |
author |
author2 |
Luchko, Yu. Rodrigues, M. M. Vieira, N. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
IC-Online |
dc.contributor.author.fl_str_mv |
Ferreira, M. Luchko, Yu. Rodrigues, M. M. Vieira, N. |
dc.subject.por.fl_str_mv |
Time-fractional diffusion-wave operator Eigenfunctions; Caputo fractional derivatives; Generalized hypergeometric series. Eigenfunctions Caputo fractional derivatives Generalized hypergeometric series |
topic |
Time-fractional diffusion-wave operator Eigenfunctions; Caputo fractional derivatives; Generalized hypergeometric series. Eigenfunctions Caputo fractional derivatives Generalized hypergeometric series |
description |
In this paper, we present some new integral and series representations for the eigenfunctions of the multidimensional time-fractional diffusion-wave operator with the time-fractional derivative of order $\beta \in ]1,2[$ defined in the Caputo sense. The integral representations are obtained in form of the inverse Fourier-Bessel transform and as double contour integrals of the Mellin-Barnes type. Concerning series expansions, the eigenfunctions are expressed as the double generalized hypergeometric series for any $\beta \in ]1,2[$ and as Kamp\'{e} de F\'{e}riet and Lauricella series in two variables for the rational values of $\beta$. The limit cases $\beta=1$ (diffusion operator) and $\beta=2$ (wave operator) as well as an intermediate case $\beta=\frac{3}{2}$ are studied in detail. Finally, we provide several plots of the eigenfunctions to some selected eigenvalues for different particular values of the fractional derivative order $\beta$ and the spatial dimension $n$. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-06 2020-12-06T00:00:00Z 2021-12-01T01:30:15Z |
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/10400.8/5523 |
url |
http://hdl.handle.net/10400.8/5523 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Ferreira, M., Luchko, Yu., Rodrigues, M.M., Vieira, N., Eigenfunctions of the time‐fractional diffusion‐wave operator. Math Meth Appl Sci. 2021; 44(2): 1713–1743. https://doi.org/10.1002/mma.6874 0170-4214 https://doi.org/10.1002/mma.6874 |
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 |
Wiley Online Library |
publisher.none.fl_str_mv |
Wiley Online Library |
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 |
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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) |
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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1799136983498358784 |