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 x-direction are analyzed in detail.

中文翻译：

---

分布有序时间分数双相位滞后模型下梳状结构中的记忆依赖异常扩散

本文考虑一种新颖的分布式有序时间分数双相位滞后模型来分析梳状结构中的异常扩散，该模型在医学和生物学中具有广泛的应用。新提出的构成模型是双相位滞后模型的推广，其中考虑了具有由权重系数控制的记忆特性的时间分数导数的谱，并且制定的控制方程包含扩散和波动特性。利用L1公式对时间Caputo分数导数进行离散化，利用有限差分法对模型进行离散化，并将相关数值结果绘制成图形。通过添加源项，定义了一个精确解来验证数值格式的正确性，并给出了空间方向误差的收敛顺序。最后，研究了粒子分布的动态特性以及所涉及的参数对粒子总数的影响。X方向进行详细分析。