The methanol transport through the porous media, e.g., pelletized zeolite-based catalyst, was investigated. Standard Fickian diffusion equation was found to be inapplicable to a description of the experimental mass transfer kinetics. The diffusion equation with the fractional-order temporal and spatial derivatives was used in order to fit the experimental data. It is demonstrated that only the diffusion equation, which contains the time-fractional derivative or both, space-time-fractional derivatives, may thoroughly describe the experimental data. The measured time-fractional order is 0.85, which reveals the non-Fickian sub-diffusive transport through the pellet. The obtained fractional order allows the application of the continuous-time random walk model as a physical ground for the explanation of the measured non-Fickian transport. Contrary, using the space-fractional diffusion equation for the experimental data description leads to the inconsistent results similarly to the standard diffusion equation. The obtained findings reveal that the diffusate flux and the flux conservation law cannot be purely space fractional.