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

  • 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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Author:Kai Diethelm, Virginia Kiryakova, Yuri Luchko, José A. Tenreiro Machado, Vasily E. Tarasov
DOI:https://doi.org/https://doi.org/10.1007/s11071-021-07158-9
ISSN:1573-269X
Parent Title (English):Nonlinear Dynamics
Document Type:Article
Language:English
Date of first Publication:2022/01/15
Publishing Institution:Hochschule für Angewandte Wissenschaften Würzburg-Schweinfurt
Release Date:2022/02/14
Tag:fractional calculus
Volume:107
First Page:3245
Last Page:3270
Institutes and faculty:Fakultäten / Fakultät für angewandte Natur- und Geisteswissenschaften
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 512 Algebra
Regensburger Klassifikation:Mathematik
Open access colour:Hybrid
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International
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