fractal structure

Deformation processes in media with fractal structure have been studied. At present, research on the construction of mathematical methods and models of interconnected deformation-relaxation and heatmass transfer processes in environments with a fractal structure is at an early stage. There are a number of unsolved problems, in particular, the problem of correct and physically meaningful setting of initial and boundary conditions for nonlocal mathematical models of nonequilibrium processes in environments with fractal structure remains unsolved.

In the work, on the basis of the apparatus of fractional integro-differentiation, the mathematical models of heat-and-moisture transfer and of deformation-relaxation processes in the medium with "memory" effects and self-organization are constructed.  Numerical implementation of the mathematical models of heat-transfer and moisture-transfer is based on the adaptation of the predictor-corrector method.  That is why the mathematical models obtained in this work are in a finite-difference form.  For the explicit difference scheme, the stability conditions are determined on the basis of the met