Trends, directions for further research, and some open problems of fractional calculus

Detalhes bibliográficos
Autor(a) principal: Diethelm, Kai
Data de Publicação: 2022
Outros Autores: Kiryakova, Virginia, Luchko, Yuri, Tenreiro Machado, J. A., Tarasov, Vasily E.
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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spelling 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
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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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
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