Steady-state heat conduction in a medium with spatial non-singular fading memory derivation of Caputo-Fabrizio space-fractional derivative from cattaneo concept with jeffrey's kernel and analytical solutions
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2017-01-01
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Abstract
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.