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This paper is devoted to the study of the flatness property of lineartime-invariant fractional systems. In the framework of polynomial matrices ofthe fractional derivative operator, we give a characterization of fractionallyflat outputs and a simple algorithm to compute them. We also obtain acharacterization of the so-called fractionnally $0$-flat outputs. We thenpresent an application to a two dimensional heated metallic sheet, whosedynamics may be approximated by a fractional model of order 1/2. The trajectoryplanning of the temperature at a given point of the metallic sheet is obtainedthanks to the fractional flatness property, without integrating the systemequations. The pertinence of this approach is discussed on simulations.

Flatness For Linear Fractional Systems With Application to a Thermal System