In trajectory planning, flatness is used to compute inputs generating suitable trajectories, without using any integration. The flatness property of linear controllable time-invariant fractional systems is studied. The formalism of polynomial matrix of the fractional differential operator is used leading to the characterization of fractionally flat outputs. The so-called defining matrices, which are transformations that express all system variables in function of the fractionally flat outputs and a finite number of their time derivatives, are introduced and characterized in this fractional context. Flatness of fractional systems is then applied to the trajectory planning of a real thermal experiment. MSC 2010 : 26A33, 34A08, 60G22