  The paper deals with the fundamental problem of a modeling of the physical,
in particular, thermal hydraulic processes, in various media of fractal
structure of the natural, technological and technical systems and devices. The
examples of a few complex systems (mainly, the physical processes) are shown as
the different fractal structures, e.g. the ones obtained by cooling and
solidification of the multiphase mixtures. Some materials reveal the structural
features having a significant influence on the behaviors of these materials.
The thermal hydraulic processes which are going during a melts cooling, with
the further water and steam flow through a porous or a channeled media, are
presenting the characteristic examples. The best models of the thermal
hydraulic and other physical processes in such fractal media should be the ones
based on the fractional differential equations. An order of the fractional
derivatives in time and space may change in the process. For example, by a
cooling of a melt, with a change of the fractal properties of the system, it is
going as follows: first, the vapor, water, melt mixture is interacting, then a
formation of the solid structure is performing due to solidification of a melt,
and a vapor flows through the permeable structure developed in a process. The
dynamically changing fractal systems (dynamic fractals) must be modeled by the
corresponding equations changing according to the evolving process. Therefore,
it is not surprising that so far some of such tasks have not been properly
resolved even in a simplified formulation. There are many similar problems in
the modern physics, technology, etc., which are discussed in the paper.
