In this paper, the problem of constructing the Lie point symmetries group of the nonlinear partial differential equation appeared in mathematical physics known as the generalized KdV-Like equation is discussed. By using the Lie symmetry method for the generalized KdV-Like equation, the point symmetry operators are constructed and are used to reduce the equation to another fractional ordinary differential equation based on Erdélyi-Kober differential operator. The symmetries of this equation are also used to construct the conservation Laws by applying the new conservation theorem introduced by Ibragimov. Furthermore, another type of solutions is given by means of power series method and the convergence of the solutions is provided; also, some graphics of solutions are plotted in 3D.

中文翻译：

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广义时间分数阶KdV-Like方程的Lie对称性分析，精确解和守恒律

本文讨论了构造数学上出现的非线性偏微分方程的Lie点对称群的问题，即广义KdV-Like方程。通过对广义KdV-Like方程使用Lie对称方法，构造了点对称算子，并将其简化为基于Erdélyi-Kober微分算子的另一个分数阶常微分方程。通过应用伊布拉吉莫夫提出的新的守恒定理，该方程的对称性也可用于构造守恒律。此外，通过幂级数法给出了另一种解，并给出了解的收敛性。同样，一些解决方案的图形以3D绘制。