The novel numerical solutions of conformable fractional Cahn-Hilliard equation in the presence of advection and reaction terms via the novel hybrid method

Abstract

In this paperthe novel numerical method is used to analyze the conformable fractional Cahn-Hilliard equation. The Cahn-Hilliard equation is a mathematical model employed as a crucial tool in mathematical physics, specifically for understanding phase separation phenomena such as spinodal decomposition in systems with multiple phases. This study investigates the convergence and error of the proposed future scheme. The proposed technique produces h-curves that show the series solution's convergence interval. To ascertain the efficacy and appropriateness of this technique, the error analysis has been conducted. Also, 2D and 3D graphs of the solutions were drawn. Additionally, the behavior of the graphs was commented. This technique has been shown to be simple, effective and fast. © 2025, Gumushane University. All rights reserved.