This paper declares a new spectral collocation technique to provide accurate approximate solutions of the one- and two-dimensional time and space fractional coupled Burgers’ equations (TSFCBEs) in which the fractional derivatives are defined according to Caputo’s definition. The suggested method is based on the shifted Gegenbauer polynomials (SGPs) for approximating the solution of TSFCBEs. The suggested technique reduces the considered problems to the solution of nonlinear algebraic equations (NLAEs). Moreover, the accuracy and reliability of the proposed method are confirmed through numerical examples. Finally, the obtained numerical results are compared with those previously reported in the literature.

中文翻译：

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多维分数阶时空耦合 Burgers 方程的数值研究

本文宣布了一种新的光谱搭配技术，以提供一维和二维时间和空间分数耦合伯格斯方程 (TSFCBE) 的精确近似解，其中分数导数是根据卡普托的定义定义的。建议的方法基于用于逼近 TSFCBE 解的移位 Gegenbauer 多项式 (SGP)。建议的技术将考虑的问题简化为非线性代数方程 (NLAE) 的求解。此外，通过数值算例验证了所提方法的准确性和可靠性。最后，将获得的数值结果与先前在文献中报道的结果进行比较。