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Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions

E. K. Lenzi·L. C. Malacarne·R. S. Mendes·I. T. Pedron
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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.

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E. K. Lenzi, L. C. Malacarne, R. S. Mendes, I. T. Pedron. 2002-08-16. Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions. https://doi.org/10.1016/s0378-4371(02)01495-4

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