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Exact solutions of a generalized multi-fractional nonlinear diffusion equation in radial symmetry. (English) Zbl 1182.35067

Summary: This paper is devoted to investigating exact solutions of a generalized fractional nonlinear anomalous diffusion equation in radial symmetry. The presence of external force and absorption is also considered. We first investigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones. In both situations, we obtain the corresponding exact solutions, and the solutions found here can have a compact behavior or a long tailed behavior.

MSC:

35C05 Solutions to PDEs in closed form
35R11 Fractional partial differential equations
35K57 Reaction-diffusion equations
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