Chaos in Fractional Order Logistic Model

The chaotic property of nonlinear dynamic systems are better characterized using a non integer dynamic model based on fractional calculus or differentiation or integration of non integer order. Dynamical system at fractional order have attracted increasingly in recent years. In this paper we investigate the fractional order of logistic equation on the basis of fractional calculus. The chaotic behavior in fractional order is identified by Lyapunov exponent for the order frac12 and frac14. The numerical results show the positive Lyapunov exponent as an indication that the system is chaotic at fractional order.