Approximate and generalized solutions of conformable type Coudrey–Dodd–Gibbon–Sawada–Kotera equation

Abstract

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 [Formula: see text]. Furthermore, residual power series method (RPSM) and [Formula: see text]-homotopy analysis method ([Formula: see text]-HAM) 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, [Formula: see text]-curve for [Formula: see text]-HAM and the effects of fractional order on the solution profiles.