In this paper, a new numerical technique implements on the time-space pseudospectral method to approximate the numerical solutions of nonlinear time- and space-fractional coupled Burgers’ equation. This technique is based on orthogonal Chebyshev polynomial function and discretizes using Chebyshev–Gauss–Lobbato (CGL) points. Caputo–Riemann–Liouville fractional derivative formula is used to illustrate the fractional derivatives matrix at CGL points. Using the derivatives matrices, the given problem is reduced to a system of nonlinear algebraic equations. These equations can be solved using Newton–Raphson method. Two model examples of time- and space-fractional coupled Burgers’ equation are tested for a set of fractional space and time derivative order. The figures and tables show the significant features, effectiveness, and good accuracy of the proposed method.

本文在时空伪谱方法上实现了一种新的数值技术，用于近似非线性时空分数耦合的Burgers方程的数值解。该技术基于正交的Chebyshev多项式函数，并使用Chebyshev–Gauss–Lobbato（CGL）点离散化。Caputo–Riemann–Liouville分数阶导数公式用于说明CGL点处的分数导数矩阵。使用导数矩阵，给定的问题被简化为非线性代数方程组。这些方程可以使用牛顿-拉夫森法求解。对于一组分数空间和时间导数阶，测试了时间和空间分数耦合的Burgers方程的两个模型示例。这些图和表格显示了重要的功能，有效性，