Memory dependent anomalous diffusion in comb structure under distributed order time fractional dual-phase-lag model

Abstract

This paper considers a novel distributed order time fractional dual-phase-lag model to analyze the anomalous diffusion in a comb structure, which has a widespread application in medicine and biology. The newly proposed constitution model is a generalization of the dual-phase-lag model, in which a spectrum of the time fractional derivatives with the memory characteristic governed by the weight coefficient is considered and the formulated governing equation contains both the diffusion and wave characteristics. With the L1-formula to discrete the time Caputo fractional derivatives, the finite difference method is used to discretize the model and the related numerical results are plotted graphically. By adding a source term, an exact solution is defined to verify the correctness of the numerical scheme and the convergence order of the error in spatial direction is presented. Finally, the dynamic characteristics of the particle distributions and the effects of involved parameters on the total number of particles in the [Formula: see text]-direction are analyzed in detail.