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

Author:

Diethelm KaiORCID,Kiryakova VirginiaORCID,Luchko YuriORCID,Machado J. A. TenreiroORCID,Tarasov Vasily E.ORCID

Abstract

AbstractThe 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.

Funder

Hochschule für angewandte Wissenschaften Würzburg-Schweinfurt

Publisher

Springer Science and Business Media LLC

Subject

Electrical and Electronic Engineering,Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Control and Systems Engineering

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