Deniz S.2024-07-222024-07-22202101704214http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/13551The Allen-Cahn model equation is extended to the fractional form by using Atangana-Baleanu derivative. The modified nonlinear equation is analyzed via optimal perturbation iteration technique and Laplace transform. Some new analytical approximate solutions are derived for different cases of order α. Absolute residual errors of different order of approximations are presented to check the effectiveness and power of the proposed method and new derivative. © 2019 John Wiley & Sons, Ltd.EnglishLaplace transformsNonlinear equationsPerturbation techniquesAllen-CahnAnalytical approximate solutionFractional derivativesIteration methodIteration techniquesModel equationsOptimal perturbationSemi-analytical analysisIterative methodsConference paper10.1002/mma.5892