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 Jeffrey’s 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 Caputo-Fabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories.