Abstract
Anomalous diffusion on a comb structure consisting of a one-dimensional backbone and lateral branches (teeth) of random length is considered. A well-defined classification of the trajectories of random walks reduces the original problem to an analysis of classical diffusion on the backbone, where, however, the time of this process is a random quantity. Its distribution is dictated by the properties of the random walks of the diffusing particles on the teeth. The feasibility of applying mean-field theory in such a model is demonstrated, and the equation for the Green’s function with a partial derivative of fractional order is obtained. The characteristic features of the propagation of particles on a comb structure are analyzed. We obtain a model of an effective homogeneous medium in which diffusion is described by an equation with a fractional derivative with respect to time and an initial condition that is an integral of fractional order.
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Zh. Éksp. Teor. Fiz. 114, 1284–1312 (October 1998)
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Lubashevskii, I.A., Zemlyanov, A.A. Continuum description of anomalous diffusion on a comb structure. J. Exp. Theor. Phys. 87, 700–713 (1998). https://doi.org/10.1134/1.558712
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DOI: https://doi.org/10.1134/1.558712