Comparison of two reliable methods to solve fractional Rosenau-Hyman equation

摘要

In this study, we examine the numerical solutions of the time-fractional Rosenau-Hyman equation, which is a KdV-like model. This model demonstrates the formation of patterns in liquid drops. For this purpose, two reliable methods, residual power series method (RPSM) and perturbation-iteration algorithm (PIA), are used to obtain approximate solutions of the model. The fractional derivative is taken in the Caputo sense. Obtained results are compared with each other and the exact solutions both numerically and graphically. The outcome shows that both methods are easy to implement, powerful, and reliable. So they are ready to implement for a variety of partial fractional differential equations.