The Efficient Robust Conformable Methods for Solving the Conformable Fractional Cahn-Allen Equation

This study focuses on the novel conformable methods employed to obtain new numerical solutions for the Cahn-Allen equation with conformable fractional derivatives. One of the two distinct methods put forth is the Cq-HATM, a hybrid technique that integrates the q-homotopy analysis transform method with the Laplace transform, utilizing the definition of conformable derivative. The CHPETM is a hybrid technique that combines the homotopy perturbation method with the Elzaki transform (ET). New numerical solutions of the conformal fractional differential Cahn-Allen equation were obtained using CHPETM and Cq-HATM. The computer simulations have been conducted in order to provide validation for the efficacy and reliability of the proposed methods. Upon performing a comparative analysis between the exact solutions and the solutions obtained through the novel methods, it becomes evident that both of these approaches exhibit simplicity, efficacy, and proficiency in addressing nonlinear conformable time-fractional coupled systems.