A model is proposed for the description of diffusion-controlled adsorption kinetics on fractal surfaces. This model is based on a constitutive equation between the mass flux and the concentration gradient of the adsorbing species expressed in terms of a Riemann-Liouville (fractional) operator of noninteger order nu. The order nu depends on the fractal dimension d(f) of the adsorbent surface, nu = d(f)-d(T), d(T) being its topological dimension. The model is compared with Monte Carlo simulations and with the approach proposed by Seri-Levy and Avnir and displays a good level of agreement with Monte Carlo data over all time scales.