Some new properties and applications of a fractional Fourier transform
Autor(a) principal: | |
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Data de Publicação: | 2017 |
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/10773/17231 |
Resumo: | In this paper, we deal with the fractional Fourier transform in the form introduced a little while ago by the first named author and his coauthors. This transform is closely connected with the Fractional Calculus operators and has been already employed for solving of both the fractional diffusion equation and the fractional Schrödinger equation. In this paper, we continue the investigation of the fractional Fourier transform, and in particular prove some new operational relations for a linear combination of the left- and righthand sided fractional derivatives. As an application of the obtained results, we provide a schema for solving the fractional differential equations with both leftand right-hand sided fractional derivatives without and with delays and give some examples of realization of our method for several fractional differential equations. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Some new properties and applications of a fractional Fourier transformFractional Fourier transformOperational relationsFractional differential equationsOperational propertiesLeft- and right- hand sided fractional derivativesFractional differential equations with delaysIn this paper, we deal with the fractional Fourier transform in the form introduced a little while ago by the first named author and his coauthors. This transform is closely connected with the Fractional Calculus operators and has been already employed for solving of both the fractional diffusion equation and the fractional Schrödinger equation. In this paper, we continue the investigation of the fractional Fourier transform, and in particular prove some new operational relations for a linear combination of the left- and righthand sided fractional derivatives. As an application of the obtained results, we provide a schema for solving the fractional differential equations with both leftand right-hand sided fractional derivatives without and with delays and give some examples of realization of our method for several fractional differential equations.Ilirias Publications2017-04-12T17:35:06Z2017-01-01T00:00:00Z2017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/17231eng2217-4303Rodrigues, M. ManuelaLuchko, Yuriinfo: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:RCAAP2024-02-22T11:32:28Zoai:ria.ua.pt:10773/17231Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:52:13.579481Repositório 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 |
Some new properties and applications of a fractional Fourier transform |
title |
Some new properties and applications of a fractional Fourier transform |
spellingShingle |
Some new properties and applications of a fractional Fourier transform Rodrigues, M. Manuela Fractional Fourier transform Operational relations Fractional differential equations Operational properties Left- and right- hand sided fractional derivatives Fractional differential equations with delays |
title_short |
Some new properties and applications of a fractional Fourier transform |
title_full |
Some new properties and applications of a fractional Fourier transform |
title_fullStr |
Some new properties and applications of a fractional Fourier transform |
title_full_unstemmed |
Some new properties and applications of a fractional Fourier transform |
title_sort |
Some new properties and applications of a fractional Fourier transform |
author |
Rodrigues, M. Manuela |
author_facet |
Rodrigues, M. Manuela Luchko, Yuri |
author_role |
author |
author2 |
Luchko, Yuri |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Rodrigues, M. Manuela Luchko, Yuri |
dc.subject.por.fl_str_mv |
Fractional Fourier transform Operational relations Fractional differential equations Operational properties Left- and right- hand sided fractional derivatives Fractional differential equations with delays |
topic |
Fractional Fourier transform Operational relations Fractional differential equations Operational properties Left- and right- hand sided fractional derivatives Fractional differential equations with delays |
description |
In this paper, we deal with the fractional Fourier transform in the form introduced a little while ago by the first named author and his coauthors. This transform is closely connected with the Fractional Calculus operators and has been already employed for solving of both the fractional diffusion equation and the fractional Schrödinger equation. In this paper, we continue the investigation of the fractional Fourier transform, and in particular prove some new operational relations for a linear combination of the left- and righthand sided fractional derivatives. As an application of the obtained results, we provide a schema for solving the fractional differential equations with both leftand right-hand sided fractional derivatives without and with delays and give some examples of realization of our method for several fractional differential equations. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-04-12T17:35:06Z 2017-01-01T00:00:00Z 2017 |
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/10773/17231 |
url |
http://hdl.handle.net/10773/17231 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2217-4303 |
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 |
Ilirias Publications |
publisher.none.fl_str_mv |
Ilirias Publications |
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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1799137572393320448 |