Progress in Fractional Differentiation & Applications

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Saudi Arabia


The research aims to propose a new non-integer order model to analyse the chaotic behaviour of a biological snap oscillator. The suggested model consists of a newly developed fractional derivative with Mittag-Leffler kernel. To investigate the model, the time- domain response and the phase portrait are considered. In addition, a powerful numerical method is employed to implement the model in an appropriate precise manner. The existence of chaotic attractors are shown by some simulations and experiments. Finally, to control the chaos, a stabilizing controller is designed and its effectiveness is illustrated and verified.

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