Using the new trend of fractional differentiation based on the concept of
exponential decay law, the Cattaneo model of diffusion in elastic medium was
extended by Hristov. This model displays more physical properties than the
first version. However no solution of this new equation is suggested in the
literature. Therefore, this paper is devoted to the analysis of numerical
solution of the Cattaneo-Hristov model with non-singular fading memory.