Trends, directions for further research, and some open problems of fractional calculus
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/10400.22/23813 |
Resumo: | The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future evolution, or, at least, the challenges identified in the scope of advanced research works. This paper gives a vision about the directions for further research as well as some open problems of FC. A number of topics in mathematics, numerical algorithms and physics are analyzed, giving a systematic perspective for future research. |
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Trends, directions for further research, and some open problems of fractional calculusFractional calculusSonine kernelsGeneral fractional integrals and derivativesFractional differential equationsNumerical solutionFractional dynamicsThe area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future evolution, or, at least, the challenges identified in the scope of advanced research works. This paper gives a vision about the directions for further research as well as some open problems of FC. A number of topics in mathematics, numerical algorithms and physics are analyzed, giving a systematic perspective for future research.SpringerRepositório Científico do Instituto Politécnico do PortoDiethelm, KaiKiryakova, VirginiaLuchko, YuriTenreiro Machado, J. A.Tarasov, Vasily E.2023-10-31T12:22:03Z20222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/23813eng10.1007/s11071-021-07158-9info: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:RCAAP2023-11-08T01:46:31Zoai:recipp.ipp.pt:10400.22/23813Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:26:14.795680Repositório 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 |
Trends, directions for further research, and some open problems of fractional calculus |
title |
Trends, directions for further research, and some open problems of fractional calculus |
spellingShingle |
Trends, directions for further research, and some open problems of fractional calculus Diethelm, Kai Fractional calculus Sonine kernels General fractional integrals and derivatives Fractional differential equations Numerical solution Fractional dynamics |
title_short |
Trends, directions for further research, and some open problems of fractional calculus |
title_full |
Trends, directions for further research, and some open problems of fractional calculus |
title_fullStr |
Trends, directions for further research, and some open problems of fractional calculus |
title_full_unstemmed |
Trends, directions for further research, and some open problems of fractional calculus |
title_sort |
Trends, directions for further research, and some open problems of fractional calculus |
author |
Diethelm, Kai |
author_facet |
Diethelm, Kai Kiryakova, Virginia Luchko, Yuri Tenreiro Machado, J. A. Tarasov, Vasily E. |
author_role |
author |
author2 |
Kiryakova, Virginia Luchko, Yuri Tenreiro Machado, J. A. Tarasov, Vasily E. |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
Diethelm, Kai Kiryakova, Virginia Luchko, Yuri Tenreiro Machado, J. A. Tarasov, Vasily E. |
dc.subject.por.fl_str_mv |
Fractional calculus Sonine kernels General fractional integrals and derivatives Fractional differential equations Numerical solution Fractional dynamics |
topic |
Fractional calculus Sonine kernels General fractional integrals and derivatives Fractional differential equations Numerical solution Fractional dynamics |
description |
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future evolution, or, at least, the challenges identified in the scope of advanced research works. This paper gives a vision about the directions for further research as well as some open problems of FC. A number of topics in mathematics, numerical algorithms and physics are analyzed, giving a systematic perspective for future research. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022 2022-01-01T00:00:00Z 2023-10-31T12:22:03Z |
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/10400.22/23813 |
url |
http://hdl.handle.net/10400.22/23813 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1007/s11071-021-07158-9 |
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: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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1799134144609910784 |