The average probability density P(r,t) of random walks on fractals is revisited within the continuous-time random walks formalism. Corrections to the accepted asymptotic stretched Gaussian decay of P(r,t) of the form r alpha are discussed. It is shown that P(r,t) obeys a diffusion equation with a fractional time derivative asymptotically, and predictions about the value of alpha are presented.
Roman, H., Alemany, P. (1994). Continuous-time random walks and the fractional diffusion equation. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 27(10), 3407-3410 [10.1088/0305-4470/27/10/017].
Continuous-time random walks and the fractional diffusion equation
Roman H. E.;
1994
Abstract
The average probability density P(r,t) of random walks on fractals is revisited within the continuous-time random walks formalism. Corrections to the accepted asymptotic stretched Gaussian decay of P(r,t) of the form r alpha are discussed. It is shown that P(r,t) obeys a diffusion equation with a fractional time derivative asymptotically, and predictions about the value of alpha are presented.
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