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Starting from the Riemann-Liouville derivative, many authors have built theirown notion of fractional derivative in order to avoid some classicaldifficulties like a non zero derivative for a constant function or a rathercomplicated analogue of the Leibniz relation. Discussing in full generality theexistence of such operator over continuous functions, we derive someobstruction Lemma which can be used to prove the triviality of some operatorsas long as the linearity and the Leibniz property are preserved. As anapplication, we discuss some properties of the Jumarie's fractional derivativeas well as the local fractional derivative. We also discuss the chain ruleproperty in the same perspective.

Comments on various extensions of the Riemann-Liouville fractional derivatives : about the Leibniz and chain rule properties