Journal
CHAOS SOLITONS & FRACTALS
Volume 89, Issue -, Pages 447-454Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2016.02.012
Keywords
Atangana-Baleanu derivatives; Integral transform operator; Uniqueness; Chaos
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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. (C) 2016 Elsevier Ltd. All rights reserved.
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