Exact solutions for a generalized nonlinear fractional Fokker–Planck equation

This paper is devoted to investigating a generalized nonlinear Fokker–Planck diffusion equation with external force and absorption. We first investigate the integer nonlinear anomalous diffusion, and we obtain the corresponding exact solution expressed by qq-exponential function. The solutions of nonlinear diffusion equation with one-fractional derivative and multi-fractional derivative are also studied in detail, and the solutions can have a compact behavior or a long tailed behavior.