On some fractal differential equations of mathematical models of catastrophic situations (Q362471)

Using Pearson's differential equation and the Kolmogorov diffusion equation, the author studies non-local differential equations. Evolution laws for the distribution densities of certain random variables are obtained, as well as the determination of transition functions of densities of non-Markov processes and Brownian motion. Major tools are the fundamental solution of the fractional diffusion equation and the introduction of the density of a generalized Pearson distribution. A power law for catastrophic processes is derived.