Abstract

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

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