Tempered fractional diffusion in comb-like structures with numerical investigation

Abstract

This paper presents two models for describing anomalous transport in comb-like structures. First, we analytically solve the tempered fractional diffusion model using the Laplace-Fourier technique. The probability distributions along the backbone (x-axis) and branches (y-axis) are represented by the M-Wright and Fox’s H functions. The probability distributions are illustrated according to the order of the time-fractional derivative α and the so-called tempered parameter λ. Additionally, we determine the mean square displacement to classify the degree of diffusivity in the comb structure based on the values of the time-fractional and tempered orders. Second, we introduce a power-law time-dependent diffusion coefficient as an extension of the comb-like models and investigate the solution of via numerical simulation. Then, we explore the connection between the presence of a time-dependent diffusion coefficient and anomalous transport based on the particle density and mean square displacement.