, Volume 104, Issue 5-6, pp 1349-1387

Spectral Analysis of Fractional Kinetic Equations with Random Data

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Abstract

We present a spectral representation of the mean-square solution of the fractional kinetic equation (also known as fractional diffusion equation) with random initial condition. Gaussian and non-Gaussian limiting distributions of the renormalized solution of the fractional-in-time and in-space kinetic equation are described in terms of multiple stochastic integral representations.