This paper develops the approximate solution of the two-dimensional space-time fractional diffusion equation. Firstly, the time-fractional derivative is discretized with a scheme of order \({\mathcal {O}}({\delta \tau }^{2-\alpha }),~ 0<\alpha <1\) . Then, the Chebyshev spectral collocation of the third kind is implemented to approximate spatial variables and to obtain full discretization of the equation. Moreover, the unconditional stability and convergence of the proposed method are shown in the perspective \(H^{2}\)-norm. Two numerical examples are presented to verify the effectiveness and the accuracy of the proposed method. The comparison between our obtained numerical results and the results of existing schemes in the literature shows that the proposed method is more reliable and precise.

本文提出了二维时空分数扩散方程的近似解。首先，用分数阶\（{\ mathcal {O}}（{\ delta \ tau} ^ {2- \ alpha}，〜0 <\ alpha <1 \）的时间离散导数。然后，执行第三种Chebyshev频谱搭配以近似空间变量并获得方程的完全离散化。此外，从\（H ^ {2} \）的角度显示了该方法的无条件稳定性和收敛性。-规范。通过两个数值例子验证了所提方法的有效性和准确性。将我们获得的数值结果与文献中现有方案的结果进行比较表明，该方法更可靠，更精确。