Trends, Directions for Further Research, and Some Open Problems of Fractional Calculus

TL;DR

This paper reviews the current state and future challenges of fractional calculus, highlighting open problems and potential research directions across mathematics, algorithms, and physics.

Contribution

It provides a systematic overview of the development, open issues, and future research directions in fractional calculus.

Findings

Identification of key open problems in FC

Analysis of trends across mathematics, algorithms, and physics

Suggestions for future research directions

Abstract

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.