Hankel operators for fractional-order systems

This paper applies the theory of a Hankel operators to fractional-order systems. It is shown that the Hankel operator approach to fractional-order systems inherently accounts for the difficulty in the initializion problem for fractional-order differential equations. The integralequation approach also verifies that the range of the Hankel operator is infinite dimensional, so a finite number of initial conditions is insufficient to account for the effect of the past behaviour on the future output of the fractional-order system. © 2008 Lavoisier, Paris.