Exact time-dependent solutions of the Renyi Fokker–Planck equation and the Fokker–Planck equations related to the entropies proposed by Sharma and Mittal

Exact time-dependent solutions representing generalized one-dimensional Ornstein–Uhlenbeck processes are derived from nonlinear Fokker–Planck equations and the corresponding diffusion processes are studied. The corresponding systems are related to the Renyi entropy and entropies proposed by Sharma and Mittal. In the former case normal diffusion is found with a diffusion rate depending on the order of the Renyi entropy. In the latter case we find anomalous diffusion processes.