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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

Hristov Jordan (University of Chemical Technology and Metallurgy, Department of Chemical Engineering, Sofia, Bulgaria)

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.

Keywords: non-linear diffusion, non-singular fading memory, Jeffrey kernel, Caputo-Fabrizio derivative integral balance approach