On some fractal differential equations of mathematical models of catastrophic situations

On the basis of the Pearson and Kolmogorov equations, we suggest and study nonlocal differential equations that permit one to obtain evolution laws for the distribution density of random variables, determine the transition function of densities of non-Markov processes and Brownian motion via the fundamental solution of the fractal diffusion equation, introduce the notion of density of a generalized Pearson distribution as an analog of the equation of exponential growth in fractional calculus, and derive a power law for catastrophic processes (in particular, floods) as the solution of a modified Cauchy problem for a loaded fractional partial differential equation of order less than unity.