Solute transit or travel time distributions (TTDs) in catchments are relevant to both hydrochemical response and inference of hydrologic mechanisms. Long-tailed TTDs and fractal scaling behavior of stream concentration power spectra (~1/frequency, or 1/frequency to a power < 2) are widely observed in catchment studies. 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 fractal scaling and long-tailed TTDs. The theoretical concentration power spectra exhibit fractal scaling, and the corresponding TTDs resemble a gamma distribution. The tails of the TTDs are influenced by accessible matrix width, exhibiting a sustained power-law (rather than exponential) decline for large matrix widths. Application to an experimental catchment shows that theoretical spectra match previously reported power spectral estimates derived from concentration measurements.