The distributed-order model is equivalent to weighting the fractional-order model on a given interval. In this paper, a double time-distributed order Maxwell model is developed and formulated to study the characteristics of a start-up pipe flow. The numerical solution of the distributed-order governing equation is obtained by the finite difference method. In order to test the convergence of numerical solutions, the truncation error of the proposed numerical method be calculated. The characteristics of the flow and the effects of fractional parameters and weight functions on the velocity distribution are discussed in detail. By comparing the velocity distribution diagrams, it can be inferred that the distributed-order model controlled by the weight function can describe the memory and elastic properties of fluid more flexibly.

分布阶模型等价于在给定区间上对分数阶模型进行加权。在本文中，开发并制定了一个双时间分布阶 Maxwell 模型来研究启动管道流动的特性。分布阶控制方程的数值解是通过有限差分法得到的。为了检验数值解的收敛性，计算了所提出数值方法的截断误差。详细讨论了流动特性以及分数参数和权函数对速度分布的影响。通过对比速度分布图可以推断，由权函数控制的分布阶模型可以更灵活地描述流体的记忆和弹性特性。