  Starting from the Riemann-Liouville derivative, many authors have built their
own notion of fractional derivative in order to avoid some classical
difficulties like a non zero derivative for a constant function or a rather
complicated analogue of the Leibniz relation. Discussing in full generality the
existence of such operator over continuous functions, we derive some
obstruction Lemma which can be used to prove the triviality of some operators
as long as the linearity and the Leibniz property are preserved. As an
application, we discuss some properties of the Jumarie's fractional derivative
as well as the local fractional derivative. We also discuss the chain rule
property in the same perspective.
