  In this paper, a novel inversion mechanism of functional extrema model via
the differential evolution algorithms(DE), is proposed to exactly identify
time-delays fractional order chaos systems. With the functional extrema model,
the unknown time-delays, systematic parameters and fractional-orders of the
fractional chaos, are converted into independent variables of a non-negative
multiple modal functions' minimization, as a particular case of the functional
extrema model's minimization. And the objective of the model is to find their
optimal combinations by DE in the predefined intervals, such that the objective
functional is minimized. Simulations are done to identify two classical
time-delayed fractional chaos, Logistic and Chen system, both in cases with
noise and without. The experiments' results show that the proposed inversion
mechanism for time-delay fractional-order chaotic systems is a successful
methods, with the advantages of high precision and robustness.
