Application of FEM with Piecewise Mittag-Leffler Functions Basis for the Linear Elasticity Problem in Materials with Fractal Structure

Mathematical model of the linear elasticity problem for capillary-porous materials with fractal structure is constructed. Integro-differentiation apparatus of fractional order to account the fractal structure of the material in the ratios of linear elasticity was used. A variational formulation of the linear elasticity problem for capillary-porous materials with fractal structure was obtained. Using the basis of the Mittag-Leffler piecewise functions to obtain an approximate solution of the problem of finding the minimum of the full potential energy functional was proposed. For partial cases the obtained results are analyzed.