In this paper, the time-fractional coupled Burger equation under Riemann-Liouville derivative is systematically analyzed. Firstly, the Lie point symmetry is obtained by applying the Lie symmetry analysis; then by utilizing the above acquired Lie point symmetry, the similarity reductions are obtained. Through similarity reductions, the coupled time-fractional Boussinesq-Burgers equation is reduced to nonlinear fractional ordinary differential equations (FODEs), with Erdélyi-Kober fractional differential operator. Then the power series method and q-homotopy analysis method are used to obtain the approximate solutions of coupled time-fractional Boussinesq-Burgers equation in the sense of the Caputo fractional derivative. Finally, the conservation laws are derived by using Noether theorem.

本文系统分析了Riemann-Liouville导数下的时间分数耦合Burger方程。首先，应用李对称分析得到李点对称；然后利用上面得到的李点对称性，得到相似度约简。通过相似性减少，耦合时间分数Boussinesq-Burgers 方程被减少为非线性分数常微分方程（FODE），使用Erdélyi-Kober 分数微分算子。然后利用幂级数法和q-同伦分析法得到耦合时间-分数阶Boussinesq-Burgers方程在Caputo分数阶导数意义上的近似解。最后，利用诺特定理推导出守恒定律。