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

Amit Prakash and Hardish Kaur

Chaos, Solitons & Fractals, 2019, vol. 124, issue C, 134-142

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.

Keywords: Cahn–Allen model; Atangana–Baleanu derivative; Homotopy perturbation technique; Laplace transform; Fixed-point theorem (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:124:y:2019:i:c:p:134-142

DOI: 10.1016/j.chaos.2019.05.005

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