Chaos in fractional-order autonomous nonlinear systems

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Analysis of the Van der Pol Oscillator Containing Derivatives of Fractional Order (2007, background): “However, it may be of interest to consider modifications to this equation in which the dependent variable x and/or its derivatives occur to some fractional power (Arena et al. 2000 Hartley et al. 1995 Ahmad and Sprott 2003 Mickens 2002, 2003 Pereira et al. 2004 Barbosa et al. 2004).”
Control of an uncertain fractional-order Liu system via fuzzy fractional-order sliding mode control (2012, background): “Since then many papers have been published dealing with chaotic behavior in fractionalorder systems (Ahmad and Sprott, 2003; Ge and Ou, 2007; Gejji and Bhalekar, 2010; Hartley et al., 1995; Lu and Chen, 2006; Matouk, 2010; Yu et al., 2009).”
Stability analysis for nonlinear fractional-order systems based on comparison principle (2014, background): “While more and more fractional-order differential equations are encountered in the fields of physics and engineering, a problem naturally comes into being: How can we control a system involving fractional derivatives so that it can run as expected? This problem has become more attractive especially ”
Chaos in the Newton–Leipnik system with fractional order (2008, background): “Moreover, in the last decade many researchers have found that chaotic attractors indeed exist in fractional-order systems [15–20].”