Dynamic of logistic model at fractional order

In this paper we have obtain the generalized form of the logistic model to arbitrary order using fractional calculus. The model is explained the population growth. The discrete version of the model have important role in studying the chaotic dynamic. The fractional calculus is feasible to evaluate the differential and integral of non integer order. This mathematical subject is helping fine tune analysis the chaotic properties of the logistic model. The numerical results show the Lyapunov exponent at various fractional orders. The positive Lyapunov exponent is indicate that the system is chaotic at fractional order. The periodic solutions of half fractional order are also present.