Numerical-analytical method for solving the modified Сauchy problem for the fractional diffusion equation

The paper considers a numerical-analytical method for efficient search for an approximate solution of the modified Cauchy problem for a parabolic differential equation with a fractional time derivative in the sense of Riemann-Liouville, which naturally arises in the study of nonlinear features of moisture-salt transfer processes in media with a fractal structure of pore space