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Solutions of Cattaneo-Hristov model of elastic heat diffusion with Caputo-Fabrizio and Atangana-Baleanu fractional derivatives

Koca Ilknur (Mehmet Akif Ersoy University, Faculty of Sciences, Department of Mathematics, Burdur, Turkey)
Atangana Abdon (University of the Free State, Faculty of Natural and Agricultural Sciences, Institute for Groundwater Studies, Bloemfontein, South Africa)

Recently Hristov using the concept of a relaxation kernel with no singularity developed a new model of elastic heat diffusion equation based on the Caputo-Fabrizio fractional derivative as an extended version of Cattaneo model of heat diffusion equation. In the present article, we solve exactly the Cattaneo-Hristov model and extend it by the concept of a derivative with non-local and non-singular kernel by using the new Atangana-Baleanu derivative. The Cattaneo-Hristov model with the extended derivative is solved analytically with the Laplace transform, and numerically using the Crank-Nicholson scheme.

Keywords: Atangana-Baleanu derivatives, numerical approximation, Cattaneo-Hristov model, elastic media