A power-law extension of the gamma distribution is proposed as a general memory function for capturing rate limitations of retention in groundwater transport. Using moments, we show how the new memory function can be reduced to most other forms available in the literature, exactly or approximately. The proposed formulation is suitable for field scale or laboratory scale transport modeling. Rate limitation effects are illustrated for solute transport by considering the fractional mass release over a given transport scale. The equilibrium and no-retention cases set bounds for contaminant attenuation, between which the impact of rate limitations is clearly exposed.