A fractional equation for diffusion in isotropic and homogeneous fractal structures is discussed. It generalizes the fractional diffusion equation valid for d-dimensional Euclidean systems. The asymptotic behaviour of the probability density function is obtained exactly. Analytical expressions are derived for the scattering and relaxation functions, which can be studied by X-ray and neutron scattering experiments on fractals.
Roman, H., Giona, M. (1992). Fractional diffusion equation on fractals: Three-dimensional case and scattering function. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 25(8), 2107-2117 [10.1088/0305-4470/25/8/024].
Fractional diffusion equation on fractals: Three-dimensional case and scattering function
Roman H. E.;
1992
Abstract
A fractional equation for diffusion in isotropic and homogeneous fractal structures is discussed. It generalizes the fractional diffusion equation valid for d-dimensional Euclidean systems. The asymptotic behaviour of the probability density function is obtained exactly. Analytical expressions are derived for the scattering and relaxation functions, which can be studied by X-ray and neutron scattering experiments on fractals.
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