Abstract
This paper studied a two-dimensional linear equation of thermal conductivity with a fractional differentiation order and compiled a computational algorithm for its numerical solution. Fractional derivatives in space and time were represented using the Riemann—Liouville definition, and the Grunwald— Letnikov definition with a shift was used to approximate them. Based on the computational algorithm, a program was written for computer modeling of the heat exchange process in heterogeneous environments. A version of the program has been developed using OpenMP parallel computing technology. The computer model has been tested by a number of numerical experiments to solve the problem of thermal momentum propagation. Based on the modeling results, the effect of fractional differentiation order on the thermal conductivity process was studied.
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