Approximate solutions to the generalized time-fractional Ito system

In this work, we consider the time-fractional version of the well-known integrable Ito system to study the effect of its fractional index ?memory index?. A modified approach of a relatively new method called residual power series (RPS) is applied to construct an analytical solution for the fractional system. For purpose of comparison, we derive one of the classical Ito system solitary wave solution using Tanh method.