Starting with the relative entropy based on a previously proposed entropy function Sq [p] = ∫ d x p (x) × (- ln p (x))q, we find the corresponding Fisher's information measure. After function redefinition we then maximize the Fisher information measure with respect to the new function and obtain a differential operator that reduces to a space coordinate second derivative in the q → 1 limit. We then propose a simple differential equation for anomalous diffusion and show that its solutions are a generalization of the functions in the Barenblatt-Pattle solution. We find that the mean squared displacement, up to a q-dependent constant, has a time dependence according to 〈 x2 〉 ∼ K1 / q t1 / q, where the parameter q takes values q = frac(2 n - 1, 2 n + 1) (superdiffusion) and q = frac(2 n + 1, 2 n - 1) (subdiffusion), ∀ n ≥ 1. © 2009 Elsevier B.V. All rights reserved.
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