In this paper, the space-time fractional advection-diffusion equation (STFADE) is considered in the finite domain that the time and space derivatives are the Caputo fractional derivative. At first, a quadratic interpolation with convergence order $\mathcal{O}\left({\tau }^{3-\alpha }\right)$ is applied to obtain the semi-discrete in time variable. Then, the Chebyshev collocation method of the fourth kind has been used to approximate the spatial fractional derivative. In addition, the energy method has been employed to show the unconditional stability and gained convergence order of the time-discrete scheme. Finally, the accuracy of the numerical method is analyzed and showed that our method is much more accurate than existing techniques.

本文在有限域中考虑时空分数阶对流扩散方程（STFADE），即时空导数为Caputo分数阶导数。首先，具有收敛阶次的二次插值$\mathcal{哦}\left({\tau }^{3——\alpha }\right)$用于获得时间变量的半离散。然后，使用第四类切比雪夫搭配方法来逼近空间分数阶导数。此外，采用能量法显示了时间离散方案的无条件稳定性并获得了收敛阶数。最后，分析了数值方法的准确性，并表明我们的方法比现有技术更准确。