Inverse Problem for a Two-Dimensional Anomalous Diffusion Equation with a Fractional Derivative of the Riemann–Liouville Type

The article presents a method for solving the inverse problem of two-dimensional anomalous diffusion equation with Riemann–Liouville fractional-order derivative. In first part present study, authors numerical solution direct problem. For this purpose, differential scheme was developed based on alternating direction implicit method. presented accompanied by examples illustrating its accuracy. second study concerned recreating model parameters, including orders fractional derivative, in equation. Equations type can be used to describe, inter alia, heat conductivity porous materials. ant colony optimization algorithm solve investigated impact distribution measurement points, use different mesh sizes, and input data errors obtained results.