Time-fractional telegraph equation with ψ-Hilfer derivatives
Autor(a) principal: | |
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Data de Publicação: | 2022 |
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/10400.8/7514 |
Resumo: | This paper deals with the investigation of the solution of the time-fractional telegraph equation in higher dimensions with $\psi$-Hilfer fractional derivatives. By application of the Fourier and $\psi$-Laplace transforms the solution is derived in closed form in terms of bivariate Mittag-Leffler functions in the Fourier domain and in terms of convolution integrals involving Fox H-functions of two-variables in the space-time domain. A double series representation of the first fundamental solution is deduced for the case of odd dimension. The results derived here are of general nature since our fractional derivatives allow to interpolate between Riemann-Liouville and Caputo fractional derivatives and the use of an arbitrary positive monotone increasing function $\psi$ in the kernel allows to encompass most of the fractional derivatives in the literature. In the one dimensional case, we prove the conditions under which the first fundamental solution of our equation can be interpreted as a spatial probability density function evolving in time, generalizing the results of Orsingher and Beghin (2004). Some plots of the fundamental solutions for different fractional derivatives are presented and analysed, and particular cases are addressed to show the consistency of our results. |
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7160 |
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Time-fractional telegraph equation with ψ-Hilfer derivativesTime-fractional telegraph equationpsi-Hilfer fractional derivativepsi-Laplace transformSeries and integral representationsFractional momentsProbability density functionThis paper deals with the investigation of the solution of the time-fractional telegraph equation in higher dimensions with $\psi$-Hilfer fractional derivatives. By application of the Fourier and $\psi$-Laplace transforms the solution is derived in closed form in terms of bivariate Mittag-Leffler functions in the Fourier domain and in terms of convolution integrals involving Fox H-functions of two-variables in the space-time domain. A double series representation of the first fundamental solution is deduced for the case of odd dimension. The results derived here are of general nature since our fractional derivatives allow to interpolate between Riemann-Liouville and Caputo fractional derivatives and the use of an arbitrary positive monotone increasing function $\psi$ in the kernel allows to encompass most of the fractional derivatives in the literature. In the one dimensional case, we prove the conditions under which the first fundamental solution of our equation can be interpreted as a spatial probability density function evolving in time, generalizing the results of Orsingher and Beghin (2004). Some plots of the fundamental solutions for different fractional derivatives are presented and analysed, and particular cases are addressed to show the consistency of our results.ElsevierIC-OnlineVieira, NelsonFerreira, MiltonRodrigues, M. Manuela2022-092024-09-01T00:00:00Z2022-09-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/7514engN. Vieira, M. Ferreira, and M.M. Rodrigues, Time-fractional telegraph equation with psi-Hilfer derivatives, Chaos, Solitons & Fractals 162, Article 112276, 20220960-077910.1016/j.chaos.2022.112276info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-17T15:55:21Zoai:iconline.ipleiria.pt:10400.8/7514Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:50:27.771202Repositório 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 |
Time-fractional telegraph equation with ψ-Hilfer derivatives |
title |
Time-fractional telegraph equation with ψ-Hilfer derivatives |
spellingShingle |
Time-fractional telegraph equation with ψ-Hilfer derivatives Vieira, Nelson Time-fractional telegraph equation psi-Hilfer fractional derivative psi-Laplace transform Series and integral representations Fractional moments Probability density function |
title_short |
Time-fractional telegraph equation with ψ-Hilfer derivatives |
title_full |
Time-fractional telegraph equation with ψ-Hilfer derivatives |
title_fullStr |
Time-fractional telegraph equation with ψ-Hilfer derivatives |
title_full_unstemmed |
Time-fractional telegraph equation with ψ-Hilfer derivatives |
title_sort |
Time-fractional telegraph equation with ψ-Hilfer derivatives |
author |
Vieira, Nelson |
author_facet |
Vieira, Nelson Ferreira, Milton Rodrigues, M. Manuela |
author_role |
author |
author2 |
Ferreira, Milton Rodrigues, M. Manuela |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
IC-Online |
dc.contributor.author.fl_str_mv |
Vieira, Nelson Ferreira, Milton Rodrigues, M. Manuela |
dc.subject.por.fl_str_mv |
Time-fractional telegraph equation psi-Hilfer fractional derivative psi-Laplace transform Series and integral representations Fractional moments Probability density function |
topic |
Time-fractional telegraph equation psi-Hilfer fractional derivative psi-Laplace transform Series and integral representations Fractional moments Probability density function |
description |
This paper deals with the investigation of the solution of the time-fractional telegraph equation in higher dimensions with $\psi$-Hilfer fractional derivatives. By application of the Fourier and $\psi$-Laplace transforms the solution is derived in closed form in terms of bivariate Mittag-Leffler functions in the Fourier domain and in terms of convolution integrals involving Fox H-functions of two-variables in the space-time domain. A double series representation of the first fundamental solution is deduced for the case of odd dimension. The results derived here are of general nature since our fractional derivatives allow to interpolate between Riemann-Liouville and Caputo fractional derivatives and the use of an arbitrary positive monotone increasing function $\psi$ in the kernel allows to encompass most of the fractional derivatives in the literature. In the one dimensional case, we prove the conditions under which the first fundamental solution of our equation can be interpreted as a spatial probability density function evolving in time, generalizing the results of Orsingher and Beghin (2004). Some plots of the fundamental solutions for different fractional derivatives are presented and analysed, and particular cases are addressed to show the consistency of our results. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-09 2022-09-01T00:00:00Z 2024-09-01T00:00:00Z |
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/10400.8/7514 |
url |
http://hdl.handle.net/10400.8/7514 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
N. Vieira, M. Ferreira, and M.M. Rodrigues, Time-fractional telegraph equation with psi-Hilfer derivatives, Chaos, Solitons & Fractals 162, Article 112276, 2022 0960-0779 10.1016/j.chaos.2022.112276 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
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 |
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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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1799136997044912128 |