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 α. Furthermore, residual power series method (RPSM) and q-homotopy analysis method (q-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, ℏ-curve for q-HAM and the effects of fractional order on the solution profiles.

中文翻译：

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适形型 Coudrey-Dodd-Gibbon-Sawada-Kotera 方程的近似和广义解

在这项研究中，我们考虑符合型 Coudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) 方程。采用三种强大的分析方法来获得感兴趣的非线性方程的广义解。首先，使用子方程方法作为基线，获得广义封闭形式的解，并且对于任何分数阶都是精确的α. 此外，剩余功率级数法（RPSM）和q-同伦分析法（q-HAM) 然后应用来获得近似解。这些是可能的使用适形导数的一些性质。由于不需要线性化、离散化和扰动，这些近似方法非常强大和高效。进行数值模拟，显示误差值，ℏ- 曲线q-HAM 和分数阶对解决方案配置文件的影响。