Numerical investigation of a fractional diffusion model on circular comb-inward structure

In this paper, the diffusion dynamics of particles on a circular comb-inward structure with different radial and tangential mobilities are studied. The Scott-Blair time-fractional memory model is exploited to incorporate the trapping process in the diffusion. A new formulation of particle flux is proposed for which the numerical discretization is straightforward. The numerical scheme is based on the second-order L2−1_σ formula for time stepping and uses the finite difference method for spatial approximations. The influences of involved parameters on the distribution of particles and the mean-square displacement (MSD) are investigated in detail. According to the model prediction, the diffusion of particles on the ring decreases with the smaller values of the fractional order α. Results also indicate that the radial and tangential mobilities exhibit the opposite effects on the MSD of particles.