Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order

Abdon Atangana and Ilknur Koca

Chaos, Solitons & Fractals, 2016, vol. 89, issue C, 447-454

Abstract: Recently, Atangana and Baleanu proposed a derivative with fractional order to answer some outstanding questions that were posed by many researchers within the field of fractional calculus. Their derivative has a non-singular and nonlocal kernel. In this paper, we presented further relationship of their derivatives with some integral transform operators. New results are presented. We applied this derivative to a simple nonlinear system. We show in detail the existence and uniqueness of the system solutions of the fractional system. We obtain a chaotic behavior which was not obtained by local derivative.

Keywords: Atangana–Baleanu derivatives; Integral transform operator; Uniqueness; Chaos (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (125)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:89:y:2016:i:c:p:447-454

DOI: 10.1016/j.chaos.2016.02.012

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