In this paper, with the aid of the Mathematica package, several classes of exact analytical solutions for the time-fractional (2+1)-dimensional Ito equation are obtained. To analytically tackle the above equation, the Kudryashov simple equation approach and its modified form are applied. Rational, exponential-rational, periodic, and hyperbolic functions with a number of free parameters were represented by the obtained soliton solutions. Graphical illustrations with special choices of free constants and different fractional orders are included for certain acquired solutions. Both approaches include the efficiency, applicability and easy handling of the solution mechanism for nonlinear evolution equations that occur in the various real-life problems.

In this study, we consider conformable type Coudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation. Three powerful analytical methods are employed to obtain generalized solutions of the nonlinear equation of interest. First, the sub-equation method is used as baseline where generalized closed form solutions are obtained and are exact for any fractional order alpha. Furthermore, Residual power series (RPSM) and q-homotopy (q-HAM) analysis techniques are then applied to obtain approximate solutions. These are possible using some properties of conformable derivative. These approximate methods are very powerful and efficient due to the absence of the need for linearization, discretization and perturbation. Numerical simulations are carried out showing error values, h-curve for q-HAM and the effects of fractional order on the solution profiles.