The fractional power laws frequently observed in dielectric measurements were interpreted in terms of regular singular points of the underlying rate equation for the process giving rise to the dielectric response. Utilizing the fact that the experimentally determined power-law responses severely constrain the form of this rate equation, an explicit expression for the dielectric-response function was derived. This expression was found to be able to describe both relaxation and low-frequency dispersion, and it also incorporates the effects of a nonzero direct-current conductivity. The frequency-dependent dielectric susceptibility was calculated analytically and compared to experimental data obtained for the sputtered amorphous thin-film tantalum oxide, which exhibited low-frequency dispersion. The agreement between theory and experiment was good, and was, for the material studied, in fact slightly better than for the well-known Dissado-Hill model.