Through this paper, we consider the time-fractional deformed fifth-order Korteweg–de Vries (KdV) equation. First of all, we detect its symmetries by Lie group analysis with the help of Riemann–Liouville (R-L) fractional derivatives. These symmetries are employed to convert the considered equation into a fractional ordinary differential (FOD) equation in the sense of Erdélyi-Kober (E-K) fractional operator. Also, a set of new analytical solutions for the equation under study are obtained via the power series method. We test the accuracy and effectiveness of this method by providing a numerical simulation of the obtained solution and studying the effect of $\alpha$ which is represented graphically in 2D and 3D plots. Added to that, we prove the convergence of the power series solutions. Finally, the computation of the conservation laws is introduced in detail.

通过本文，我们考虑了时间分数变形五阶 Korteweg–de Vries (KdV) 方程。首先，我们借助黎曼-刘维尔 (RL) 分数阶导数通过李群分析检测其对称性。这些对称性用于将所考虑的方程转换为 Erdélyi-Kober (EK) 分数算子意义上的分数常微分 (FOD) 方程。此外，通过幂级数法获得了所研究方程的一组新解析解。我们通过对所获得的解决方案进行数值模拟并研究其效果来测试该方法的准确性和有效性$\alpha$它以 2D 和 3D 绘图的形式表示。除此之外，我们还证明了幂级数解决方案的收敛性。最后详细介绍了守恒定律的计算。