  In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210 or
arXiv:1002.0999v1 [math-ph]) we introduced a modified Fourier-Cattaneo law and
derived a non-autonomous telegraph-type heat conduction equation which has
desirable self-similar solution. Now we present a detailed in-depth analysis of
this model and discuss additional analytic solutions for different parameters.
The solutions have a very rich and interesting mathematical structure due to
various special functions.
