The fractality of the environment has a profound influence on the diffusion of molecules through a porous amorphous catalyst. Based on the fractal geometrical description of the pore morphology, the appropriate equations for multicomponent diffusion and arbitrary reaction in a fractal pore are derived. An analytical expression is found for the Knudsen diffusivity. It depends on the size of the molecule and on the adsorption fractal dimension of the catalyst surface. Fractal continuity equations are set up for a diffusing and reacting component in a pore of a uniformly active or supported catalyst. The case of a first-order reaction is studied in an analytical way. The solutions of the fractal continuity equation of the reacting component are compared with those of a smooth cylindrical pore. It follows that it is usually impossible to define an equivalent classical pore that would lead to both the same concentrations and fluxes at the pore ends, as the real fractal pore. Attention is paid to the practical validity of the application of differential equations instead of difference equations. It is shown that the approximation is almost invariably acceptable for practical problems in catalysis.