Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model

Obaid Jefain Julaighim Algahtani

Chaos, Solitons & Fractals, 2016, vol. 89, issue C, 552-559

Abstract: In 2015 Caputo and Fabrizio suggested a new operator with fractional order, this derivative is based on the exponential kernel. Earlier this year 2016 Atangana and Baleanu developed another version which used the generalized Mittag-Leffler function as non-local and non-singular kernel. Both operators show some properties of filter. However the Atangana and Baleanu version has in addition to this, all properties of fractional derivative. In this work, we aimed to represent the model by Allen–Cahn with both derivatives in order to see their difference in a real world problem. Both modified models will be solved numerically via the Crank–Nicholson scheme and their numerical simulations are presented to check the effectiveness of the both kernels.

Keywords: Atangana–Baleanu derivatives; Caputo–Fabrizio derivatives; Allen–Cahn model (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:89:y:2016:i:c:p:552-559

DOI: 10.1016/j.chaos.2016.03.026

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