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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

thermal science/thermal science

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