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Beschreibung:
A new stochastic fractal model based on a fractional Laplace equation is developed. Exact representations for the spectral and correlation functions under random boundary excitation are obtained. A randomized spectral expansion is constructed for simulation of the solution of the fractional Laplace equation. We present calculations for 2D and 3D spaces for a series of fractional parameters showing a strong memory effect: the decay of correlations is several order of magnitude less as compared to the conventional Laplace equation model.