*Heat Conduction of Fractional Cattaneo Type*

**Dusan Zorica**

Mathematical Institute

Serbian Academy of Sciences and Arts

`dusan_zorica@mi.sanu.ac.rs`

**
Abstract**: 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
, as well as
the first order space derivative of temperature with the symmetrized Caputo
space-fractional derivative of order
, 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.