TY - JOUR A1 - Diethelm, Kai A1 - Kiryakova, Virginia A1 - Luchko, Yuri A1 - Tenreiro Machado, José A. A1 - Tarasov, Vasily E. T1 - Trends, directions for further research, and some open problems of fractional calculus JF - Nonlinear Dynamics N2 - 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. KW - fractional calculus Y1 - 2022 U6 - https://doi.org/https://doi.org/10.1007/s11071-021-07158-9 SN - 1573-269X VL - 107 SP - 3245 EP - 3270 ER -