Abstract <p>A mathematical model of the formation of thunderstorms of moderate latitudes is considered, taking into account the fractal structure of the cloud environment, using the apparatus of fractional integro-differentiation. Unlike classical works, in this article, the process of electrification of hailstones in cumulonimbus clouds of temperate latitudes depends not only on the electric field strength, the charge carried away by the drop, the size and speed of the fall of the hailstone, but also on the fractal parameter (fractal dimension) of the cloud environment. The dependence of the dynamics of charging of hailstone formation in thunderstorms of temperate latitudes on the values of the fractal parameter, as well as the dependence on both constants and various values of the parameter characterizing fractal structures, is shown.</p>