  Employing a phase space which includes the (Riemann-Liouville) fractional
derivative of curves evolving on real space, we develop a restricted
variational principle for Lagrangian systems yielding the so-called restricted
fractional Euler-Lagrange equations (both in the continuous and discrete
settings), which, as we show, are invariant under linear change of variables.
This principle relies on a particular restriction upon the admissible variation
of the curves. In the case of the half-derivative and mechanical Lagrangians,
i.e. kinetic minus potential energy, the restricted fractional Euler-Lagrange
equations model a dissipative system in both directions of time, summing up to
a set of equations that is invariant under time reversal. Finally, we show that
the discrete equations are a meaningful discretisation of the continuous ones.
