This work considers a robust homotopy analysis method with a formable transform that investigates a time-fractional Rosenau-Hyman model based on a KdV-like equation having compacton solutions. Here, a novel technique that combines the homotopy analysis method with formable transformation has been implemented, called \(\eta\)-homotopy analysis formable transformation technique (\(\eta\)-HAFTT) to obtain an approximate analytical solution of the time-fractional Rosenau-Hyman equation. Finally, the \(\eta\)-HAFTT solution is compared with the available solution numerically and graphically to check the efficacy of the obtained solution. It shows that the new suggested algorithm (\(\eta\)-HAFTT) provides the approximate solutions with the least approximations having better accuracy.

这项工作考虑了一种具有可成形变换的稳健同伦分析方法，该方法基于具有紧致解的 KdV 类方程研究时间分数 Rosenau-Hyman 模型。在这里，实现了一种将同伦分析方法与可成形变换相结合的新技术，称为\(\eta\) -同伦分析可成形变换技术（\(\eta\) -HAFTT），以获得时间的近似解析解-分数Rosenau-Hyman方程。最后，将\(\eta\) -HAFTT 解决方案与可用的解决方案进行数值和图形比较，以检查所获得解决方案的有效性。它表明新的建议算法（\(\eta\)-HAFTT) 提供具有更好精度的最小近似值的近似解。