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Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws

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  • Atangana, Abdon
  • Gómez-Aguilar, J.F.

Abstract

The nature is very complex to model with mathematical equations. Some physical problems found in nature could follow the power law; other could follow the Mittag–Leffler law and other the exponential decay law. On the other hand one could observe in nature a physical problem that combines both, it is therefore important to provide a new fractional operator that could possibly be used to model such physical problem. In this paper, we suggest a fractional operator exponential-Mittag–Leffler kernel with two fractional orders. Some very useful properties are obtained. Numerical solutions were obtained for three examples proposed.

Suggested Citation

  • Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 285-294.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:285-294
    DOI: 10.1016/j.chaos.2017.03.022
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