Fractional differential equations play an essential role in describing the shallow water wave phenomena. In this article, we discussed the coupled Burgers-type equations in the sense of the fractional derivative of Riemann-Liouville. In return, a series of new results of this considered models, were obtained. In the first place, the formulation of the time fractional coupled Burgers-type equations by applying the Euler-Lagrange variational technology, was carried out. Then, the symmetry and one-parameter group of point transformations of this researched goals through the symmetry analysis scheme, were obtained. Subsequently, the time fractional coupled Burgers-type equations can be reduced into the fractional ordinary differential equations with the help of the Erdélyi-Kober fractional differential/integral operators. Next, the approximate solution and convergence analysis, were considered. At the same time, the stability analysis of the solitary wave, was also studied. Lastly, conservation laws of this discussed equations by using a new conservation theorem and nonlinear self-adjointness, were found. The series of results obtained above can provide strong support for us to reveal the mystery of the equation.

分数阶微分方程在描述浅水波现象中起着至关重要的作用。在本文中，我们讨论了 Riemann-Liouville 分数阶导数意义上的耦合 Burgers 型方程。作为回报，获得了该考虑模型的一系列新结果。首先，应用欧拉-拉格朗日变分技术建立了时间分数阶耦合伯格斯方程。然后，通过对称分析方案，得到了该研究目标的点变换的对称性和单参数群。随后，在 Erdélyi-Kober 分数阶微分/积分算子的帮助下，时间分数耦合 Burgers 型方程可以简化为分数阶常微分方程。下一个，考虑了近似解和收敛分析。同时，对孤立波的稳定性分析也进行了研究。最后，通过使用新的守恒定理和非线性自伴随性，找到了这个讨论方程的守恒律。上面得到的一系列结果可以为我们揭开方程的奥秘提供有力的支持。