# Iterative Methods for Solving Fourth and Sixth Order Time-fractional Cahn-Hillard Equation

## TL;DR

This paper introduces new iterative methods to find approximate solutions for complex fourth and sixth order time-fractional Cahn-Hilliard equations, demonstrating their effectiveness and accuracy through examples.

## Contribution

It develops and applies the new iterative method (NIM) and q-homotopy analysis method (q-HAM) to solve high-order fractional differential equations.

## Key findings

- Convergent series solutions obtained for TFCH equations.
- Methods show simplicity and high accuracy in solving nonlinear fractional equations.
- Error estimates provided when exact solutions are available.

## Abstract

This paper presents analytical-approximate solutions of the time-fractional Cahn-Hilliard (TFCH) equations of fourth and sixth-order using the new iterative method (NIM) and q-homotopy analysis method (q-HAM). We obtained convergent series solutions using these iterative methods. The simplicity and accuracy of these methods in solving strongly nonlinear fractional differential equations is displayed through the examples provided. In the case where exact solution exists, error estimates are also investigated.