No violation of the Leibniz rule. No fractional derivative

•A violation of the Leibniz rule is a basic property of fractional derivatives.•Any fractional derivative, which satisfy Leibniz rule, has order equal to one.•Fractional derivatives of non-integer orders cannot satisfy the Leibniz rule.

We demonstrate that a violation of the Leibniz rule is a characteristic property of derivatives of non-integer orders. We prove that all fractional derivatives DαDα, which satisfy the Leibniz rule Dα(fg)=(Dαf)g+f(Dαg)Dα(fg)=(Dαf)g+f(Dαg), should have the integer order α=1α=1, i.e. fractional derivatives of non-integer orders cannot satisfy the Leibniz rule.