How Many Fractional Derivatives Are There?

In this paper, we introduce a unified fractional derivative, defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained. We study the one-sided derivatives and show that most known derivatives are particular cases. We consider also some myths of Fractional Calculus and false fractional derivatives. The results are expected to contribute to limit the appearance of derivatives that differ from existing ones just because they are defined on distinct domains, and to prevent the ambiguous use of the concept of fractional derivative.

Automated summary

In this paper, a unified fractional derivative is introduced, which can generate various interesting derivative forms. The results of this study are expected to reduce derivative differences and prevent the ambiguous use of fractional derivatives.