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

被引：80
作者：
Diethelm, Kai [1 ]
Kiryakova, Virginia [2 ]
Luchko, Yuri [3 ]
Machado, J. A. Tenreiro [4 ]
Tarasov, Vasily E. [5 ]
机构：
[1] Univ Appl Sci Wurzburg Schweinfurt, Fac Appl Nat Sci & Humanities FANG, Ignaz Schon Str 11, D-97421 Schweinfurt, Germany
[2] Bulgarian Acad Sci, Inst Math & Informat, Sofia 1113, Bulgaria
[3] Berlin Univ Appl Sci & Technol, Dept Math Phys & Chem, Luxemburger Str 10, D-13353 Berlin, Germany
[4] Polytech Porto, Inst Engn, Dept Elect Engn, Rua Dr Antonio Bernardino Almeida 431, P-4249015 Porto, Portugal
[5] Natl Res Univ, Moscow Aviat Inst, Fac Informat Technol & Appl Mathemat, Moscow 125993, Russia
来源：
NONLINEAR DYNAMICS | 2022年 / 107卷 / 04期
关键词：
Fractional calculus; Sonine kernels; General fractional integrals and derivatives; Fractional differential equations; Numerical solution; Fractional dynamics; VOLTERRA INTEGRAL-EQUATIONS; FAST NUMERICAL-SOLUTION; DIFFERENTIAL-EQUATIONS; EFFICIENT COMPUTATION; EXACT DISCRETIZATION; DYNAMIC-SYSTEMS; DERIVATIVES; QUANTUM; SCHEME; MEMORY;
D O I：
10.1007/s11071-021-07158-9
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
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.
引用
收藏
页码：3245 / 3270
页数：26
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