  The quantum analogs of the derivatives with respect to coordinates q_k and
momenta p_k are commutators with operators P_k and $Q_k. We consider quantum
analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain
the quantum analogs of fractional Riemann-Liouville derivatives, which are
defined on a finite interval of the real axis, we use a representation of these
derivatives for analytic functions. To define a quantum analog of the
fractional Liouville derivative, which is defined on the real axis, we can use
the representation of the Weyl quantization by the Fourier transformation.
