We consider a fractional order viscoelasticity problem modelled by a power-law type stress relaxation function. This viscoelastic problem is a Volterra integral equation of the second kind with a weakly singular kernel where the convolution integral corresponds to fractional order differentiation/integration. We use a spatial finite element method and a finite difference scheme in time. Due to the weak singularity, fractional order integration in time is managed approximately by linear interpolation so that we can formulate a fully discrete problem. In this paper, we present a stability bound as well as a priori error estimates. Furthermore, we carry out numerical experiments with varying regularity of exact solutions at the end.

我们考虑由幂律型应力松弛函数建模的分数阶粘弹性问题。这个粘弹性问题是具有弱奇异核的第二类Volterra积分方程，其中卷积积分对应于分数阶微分/积分。我们在时间上使用空间有限元方法和有限差分方案。由于奇异性较弱，因此时间分数阶积分大约是通过线性插值来管理的，因此我们可以提出一个完全离散的问题。在本文中，我们提出了一个稳定性边界以及一个先验误差估计。此外，最后我们进行了数值实验，其中精确解的变化规律性不同。