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 $qge 0.2$ . Values of the delay time $tau $ in which chaotic behavior is observed at system order $q$ are quantitatively defined using the largest Lyapunov exponents obtained from the output time series.