No violation of the Leibniz rule. No fractional derivative

摘要

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 D~x, which satisfy the Leibniz rule D~x(fg) = (D~xf)g+f(D~xg), should have the integer order x =1, i.e. fractional derivatives of non-integer orders cannot satisfy the Leibniz rule.