Analysis and numerical simulation of fractional order Cahn–Allen model with Atangana–Baleanu derivative

Abstract

Abstract In this work, we present a fractional model of Cahn–Allen equation associated with newly introduced Atangana–Baleanu (AB) derivative of fractional order which uses Mittag–Leffler function as the non-singular and non-local kernel. The existence and uniqueness of this modified fractional model are discussed by employing the fixed-point postulate. An efficient scheme homotopy perturbation transform technique (HPTT) which is an amalgamation of homotopy perturbation technique with Laplace transform is used to examine this time-fractional phase-field model numerically. Also, convergence and error analysis of the proposed technique is presented. The numerical simulations are analyzed graphically as well as in tabulated form.