In this paper, a systematic study for finding the symmetry group classification is performed for the time-fractional Kudryashov–Sinelshchikov equation, which describes the pressure waves in liquid with gas bubbles. Using Lie symmetries, the vector fields, and invariance properties of the underlying equation with various cases are presented and then similarity reductions are obtained. Furthermore, using the new conservation theorem, conservation laws are constructed for all possible cases. Finally, based on the invariant subspace method, a variety of exact solutions are derived using the obtained invariant subspaces, including the trigonometric, exponential, and polynomial type of solutions.

在本文中，系统研究了寻找对称群分类的时间分数 Kudryashov-Sinelshchikov 方程，该方程描述了带有气泡的液体中的压力波。使用李对称性，在各种情况下给出了基础方程的向量场和不变性，然后获得相似度约简。此外，使用新的守恒定理，为所有可能的情况构建守恒律。最后，基于不变子空间方法，利用获得的不变子空间推导出各种精确解，包括三角、指数和多项式类型的解。