Solution of Time-Fractional Rosenau-Hyman Model Using a Robust Homotopy Approach via Formable Transform

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 η -homotopy analysis formable transformation technique ( η -HAFTT) to obtain an approximate analytical solution of the time-fractional Rosenau-Hyman equation. Finally, the η -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 ( η -HAFTT) provides the approximate solutions with the least approximations having better accuracy.