Non-Markovian Levy diffusion in nonhomogeneous media

Abstract

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the Lévy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.

7 pages, 2 figures

References in corpus (3)

• The scaling laws of human travel
• Macroscopic description of particle systems with non-local density-dependent diffusivity
• Directed percolation with incubation times

Cited by in corpus (1)

• Non-Markovian diffusion equations and processes: analysis and simulations