Two-parameter entropy the Sharma−Mittal functional as core family of nonlinear Fokker−Planck−Kolmogorov equations

Abstract

An important aspect related to the derivation of nonlinear power-law equations of Fokker–Planck–Kolmogorov correlated with the Sharma–Mittal entropy is analyzed in this work. In this case, the obtained diffusion equations are written in such a way that their stationary solutions are probability distributions that maximize the ShM entropy for non-extensive systems. The ansatz approach is used to obtain exact solutions of nonlinear nonstationary one-dimensional FPK equations associated with the Tsallis, Renyi, and Sharma–Mittal entropies.