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

Abstract

In this study, we examine the numerical solutions of the time-fractionalRosenau-Hyman equation, which is a KdV-like model. This model demonstratesthe formation of patterns in liquid drops. For this purpose, two reliable meth-ods, 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 eachother and the exact solutions both numerically and graphically. The outcomeshows that both methods are easy to implement, powerful, and reliable. So theyare ready to implement for a variety of partial fractional differential equations.