This paper describes a method of approximating equations with the Erdélyi--Kober fractional operator which arise in mathematical descriptions of anomalous diffusion. We prove a theorem on the exact form of the approximating series and provide an illustration by considering the fractional porous-medium equation applied to model moisture diffusion in building materials. We obtain some approximate analytical solutions of our problem which accurately fit the experimental data (better than other models found in the literature). This accuracy is also verified numerically. Since they are very quick and easy to implement, our approximations can be valuable for practitioners and experimentalists.