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Carnegie Mellon Center for Nonlinear Analysis
Heat Conduction of Fractional Cattaneo Type


Dusan Zorica
Mathematical Institute
Serbian Academy of Sciences and Arts

: In order to model heat conduction (or diffusion) in some special type of materials, we start form the Cattaneo constitutive equation. By replacing the first order time derivative of the heat flux with the Caputo time-fractional derivative of order $\alpha \in (0,1)$, as well as the first order space derivative of temperature with the symmetrized Caputo space-fractional derivative of order $\beta \in (0,1)$, we obtain the constitutive equation non-local in both time and space. We consider the system of such a constitutive equation and energy balance equation. Further, we prove the existence of the solution for the Cauchy problem, calculate the solution and compare it numerically with the results in limiting cases.