Approximated solution of Example 3.1 at <i>t</i> = 0.01.

In this article, Elzaki decomposition method (EDM) has been applied to approximate the analytical solution of the time-fractional gas-dynamics equation. The time-fractional derivative is used in the Caputo-Fabrizio sense. The proposed method is implemented on homogenous and non-homogenous cases of the time-fractional gas-dynamics equation. A comparison between the exact and approximate solutions is also provided to show the validity and accuracy of the technique. A graphical representation of all the retrieved solutions is shown for different values of the fractional parameter. The time development of all solutions is also represented in 2D graphs. The obtained results may help understand the physical systems governed by the gas-dynamics equation.本文采用埃尔扎基分解法（Elzaki Decomposition Method，EDM）对时间分数阶气体动力学方程的解析解进行近似求解，其中时间分数阶导数采用卡普托-法布里齐奥（Caputo-Fabrizio）定义。本文将所提方法应用于时间分数阶气体动力学方程的齐次与非齐次情形。同时通过精确解与近似解的对比，验证了该方法的有效性与准确性。针对分数阶参数的不同取值，给出了所有所得解的可视化图像；所有解的时间演化过程也通过二维图形进行了展示。本次研究获得的结果有助于理解由气体动力学方程所支配的物理系统。