  A Cattaneo equation for a comb structure is considered. We present a rigorous
analysis of the obtained fractional diffusion equation, and corresponding
solutions for the probability distribution function are obtained in the form of
the Fox $H$-function and its infinite series. The mean square displacement
along the backbone is obtained as well in terms of the infinite series of the
Fox $H$-function. The obtained solutions describe the transition from normal
diffusion to subdiffusion, which results from the comb geometry.
