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An original method for modeling, simulation and identification of fractional systems in the time domain is presented in this article. The basic idea is to model the fractional system by a state-space representation, where conventional integration is replaced by a fractional one with the help of a non-integer integrator. This operator is itself approximated by a N -dimensional system composed of an integrator and of a phase-lead filter. An output-error technique is used in order to estimate the parameters of the model, including the fractional order n. Simulations exhibit the properties of the identification algorithm. Finally, this methodology is applied to the modeling of the dynamics of a real heat transfer system.

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