Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions

TL;DR

This paper derives new exact solutions for a nonlinear fractional Fokker-Planck equation with specific diffusion and drift terms, exploring their connection to nonextensive statistical mechanics and Tsallis entropy.

Contribution

It introduces novel exact solution classes for a nonlinear fractional Fokker-Planck equation with power-law diffusion and complex drift, linking to Tsallis entropy.

Findings

Derived new exact solutions for the fractional Fokker-Planck equation.

Established connections between solutions and nonextensive statistical mechanics.

Discussed implications for systems described by Tsallis entropy.

Abstract

We obtain new exact classes of solutions for the nonlinear fractional Fokker-Planck-like equation partial_t rho = partial_x{D(x) partial^{mu -1}_x rho^{nu} - F(x) rho} by considering a diffusion coefficient D = D|x|^{-theta} (theta in R and D>0) and a drift force F = -k_1 x + k-bar_{gamma} x|x|^{gamma-1} (k_1, k-bar_{gamma}, gamma in R). Connection with nonextensive statistical mechanics based on Tsallis entropy is also discussed.