Iranian Journal of Science and Technology, Transactions A: Science ( IF 1.4 ) Pub Date : 2022-09-15 , DOI: 10.1007/s40995-022-01347-w Vishalkumar J. Prajapati , Ramakanta Meher
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.
中文翻译:
时间分数 Rosenau-Hyman 模型的求解使用稳健同伦方法通过可成形变换
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。