Solute travel time distributions (TTDs) in catchments are relevant to both hydrochemical response and inference of hydrologic mechanisms. Time and frequency domain methods have been employed to estimate solute TTDs and associated power spectra. Stream concentration power spectra in some catchments exhibit fractal scaling (~1/frequency, or generally, 1/frequency to a power < 2). Various mechanisms have been proposed previously for fractal scaling. In several catchments, a significant fraction of streamflow is derived from groundwater in shallow fractured bedrock, where matrix diffusion significantly influences solute transport. I present frequency and time domain theoretical analyses of solute transport to quantify the influence of matrix diffusion on solute TTDs in catchment groundwater systems. The theoretical concentration power spectra exhibit fractal scaling, and the corresponding TTDs resemble a gamma distribution. An application to the Lower Hafren catchment using site-specific parameters shows that theoretical spectra match previously reported power spectral estimates derived from concentration measurements.