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Exact solutions for a generalized nonlinear fractional Fokker-Planck equation. (English) Zbl 1181.35293
Summary: 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 \(q\)-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.

35Q84 Fokker-Planck equations
35R11 Fractional partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
35C05 Solutions to PDEs in closed form
Full Text: DOI
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