Chaotic dynamics of the fractional order nonlinear system with time delay

This paper presents the fractional order model of a nonlinear autonomous continuous-time difference-differential equation with only one variable. Numerical simulation results of the fractional order model demonstrate the existence of chaos when system order . Values of the delay time in which chaotic behavior is observed at system order are quantitatively defined using the largest Lyapunov exponents obtained from the output time series.