Semi‐analytical analysis of Allen‐Cahn model with a new fractional derivative

The 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.