An effective technique for solving generalized Cahn-Hilliard (C-H) problems.

Throughout this paper, we apply the Optimal Homotopy Asymptotic Method (OHAM) to find out the numerical solutions of the fractional Cahn-Hilliard (C-H) equation. We examine fractional order time dependent partial differential equations to assess the method's competency. In the Caputo sense, fractional-order derivatives have been applied with numerical values in the closed interval [0, 1]. The most advantage of this method is that it contains parameters that strongly control the solution series convergence. Additionally, this method greatly simplifies calculations because it does not require any linearization, discretization, or little perturbations. Approximate solutions of the C-H equation were compared with the exact solutions; moreover the results of the suggested method have been compared with those of other widely used numerical techniques, such as the Adomian decomposition analysis method. A comparison of these solutions with the exact solution shows that our method is more effective and accurate for solving nonlinear differential equations. MATLAB R2021b is utilized to generate the numerical results.