TRANSIENT HEAT DIFFUSION WITH A NON-SINGULAR FADING MEMORY From the Cattaneo Constitutive Equation with Jeffrey's Kernel to the Caputo-Fabrizio Time-Fractional Derivative

Starting from the Cattaneo constitutive relation with a Jeffreys kernel the derivation of a transient heat diffusion equation with relaxation term expressed through the Caputo-Fabrizio time fractional derivative has been developed. This approach allows seeing the physical background of the newly defined CaputoFabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories.