We investigate the performance of Brownian motors in environments governed by the "porous medium" equation partial differential(t)rho = D partial differential(x) (rho(nu-1) partial differential(x)rho), where rho is the density and D and nu positive constants. This nonlinear equation yields anomalous diffusion when nu not = 1: subdiffusion for nu > 1 and superdiffusion for nu < 1. The thermal ratchet is modeled by an overdamped Brownian particle subject to a one-dimensional, spatially periodic, asymmetric potential, modulated by time-periodic fluctuations. We scrutinize the transport properties in the adiabatic limit. The superdiffusive regime, in comparison with the normal one, exhibits transport enhancement for small amplitudes of the temporal fluctuations. Meanwhile, the subdiffusive regime displays more strident features: The flux may become forbidden in one or in both directions. As a consequence, when the blockade is unidirectional, purely directed transport occurs.