Space- and time-fractional diffusion and wave equations, fractional Fokker-Planck equations, and physical motivation

By Ralf Metzler, T. Nonnenmacher. 2002

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On the local fractional wave equation in fractal strings (2019, unknown): “0 Eβ −z βξ g ξ ð Þ dξ ð Þ; 0 < β ≤ 1: (4)”
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, methodology): “In this limit, one can obtain simple reductions of the H-function solution, in the following three cases (Metzler and Nonnenmacher 2002): (i) Cauchy propagator α = µ = 1, P(x, t) = 1 2πK11 t 1 1 + x2 /( K11 t ) (52) with the long-tailed asymptotics P(x, t) ∼ (2π)−1x−2.”