Novel approximations to the fourth-order fractional Cahn–Hillard equations: Application to the Tantawy Technique and other two techniques with Yang transform
S. A. El-Tantawy, Amnah S. Al‐Johani, Aljawhara H. Almuqrin, Adnan Khan, L. S. El‐Sherif
Abstract
This investigation employs the “Tantawy Technique,” a novel, highly accurate, and fast technique, to solve and analyze the fourth-order time-fractional Cahn–Hilliard (TFCH) models. We also implement the variational iteration transform method (VITM) and the homotopy perturbation transform method (HPTM) within the Yang transform framework to analyze the fourth-order TFCH models. These iterative procedures enable the acquisition of solutions in a convergent series. We focus on two nonlinear issues in the current investigation to demonstrate the validity and accuracy of the suggested approaches. We check the derived approximations against the exact solutions for the integer cases and then find their absolute error to ensure their accuracy and stability. The present approaches show how different fractional orders affect the profile of the derived approximations. The presented issues demonstrate the precision and effectiveness of the suggested techniques in tackling strong nonlinear fractional differential equations. Implementing the suggested methodologies indicates that as the value of the fractional parameter transitions from fractional to integer order, the result approaches the exact solution for the integer case. These methods also make it straightforward to use fractal calculus in real life. The numerical analysis results demonstrate that the proposed iterative techniques are viable and user-friendly tools with high computational efficiency when used in various physical models in science and engineering.