Some applications of fractional calculus in suppression of chaotic oscillations

This paper presents two different stabilization methods based on the fractional-calculus theory. The first method is proposed via using the fractional differentiator, and the other is constructed based on using the fractional integrator. It has been shown that the proposed techniques can be used to suppress chaotic oscillations in 3-D chaotic systems. To show the practical capability of the methods, some experimental results on the control of chaos in chaotic circuits are presented. Index Terms--Chaos, chaotic circuit, fractional-order controller, stabilization.