Levenberg-Marquardt method for restoration of layered medium key parameters

We consider the model of the anomalous diffusion process layered media exhibiting memory. We use fractional calculus as a mathematical description of such media and state the boundary value problem for the partial differential equation in fractional derivatives. We define inverse problems as the restoration of the medium key parameters including the anomalous diffusion index that correlates with the fractional dimension of the medium. The numerical approach involves numerical simulations of the process and variational methods for inverse problems. We present the numerical solutions obtained by means of the Levenberg-Marquardt method and discuss the corresponding results.