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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 $\partial_t\rho=\partial_x\{D(x)\partial^{\mu-1}_x\rho^{\nu}-F(x)\rho\}$ by considering a diffusion coefficient $D=D|x|^{-\theta}$ $(\theta\in \bbfR$ and $D>0)$ and a drift force $F=-k_1x+\bar k_{\gamma}x|x|^{\gamma-1} (k_1,\bar k_{\gamma},\gamma\in \bbfR)$. 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
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References:
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