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Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions. (English) Zbl 1008.82027
Summary: We obtain new exact classes of solutions for the nonlinear fractional Fokker-Planck-like equation t ρ= x {D(x) x μ-1 ρ ν -F(x)ρ} by considering a diffusion coefficient D=D|x| -θ (θ and D>0) and a drift force F=-k 1 x+k ¯ γ x|x| γ-1 (k 1 ,k ¯ γ ,γ). Connection with nonextensive statistical mechanics based on Tsallis entropy is also discussed.
MSC:
82C70Transport processes (time-dependent statistical mechanics)
82C31Stochastic methods in time-dependent statistical mechanics
35K55Nonlinear parabolic equations
35C05Solutions of PDE in closed form