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

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. (C) 2019 Published by Elsevier Ltd.