Structure parameter θ that reflects the dynamic character of methane in coal and fractal dimension df that reflects the static structure of coal were introduced into Fick’s model, and based on the assumption that the diffusion is memorable by introducing a parameter v, a Fractional order of diffusion model was established (the FFD Model). Several adsorption and desorption experiments on anthracite coal with different grain sizes (0.2-0.25 mm, 1-3 mm) were performed under different equilibrium pressures (1 MPa, 4 MPa) to determine the parameters and to confirm the validity of the FFD Model. On that basis, further desorption experiment of pulverized coal was conducted to validate the applicability of the FFD Model on pulverised coal. The results showed that the desorption rate of the 0.045-0.075 mm grain size coal is seven times of the 0.106-0.25 mm grain size coal. The implications of the study are for the pulverising phenomenon during the coal and gas outburst. The desorption velocity will increase rapidly, resulting in the dramatic increase of expansion energy of methane, and this further accelerates the pulverising process - a positive feedback effect between desorption velocity and dusting process. This can be used to explain the phenomenon of the gas-solid two phases flow and the piston effect during the coal and gas outburst.