A continuous/discrete fractional Noether’s theorem

► Continuous and discret fractional Lagrangian systems. ► Continuous and discrete Noether’s theorem. ► Explicit first integrals. We prove a fractional Noether’s theorem for fractional Lagrangian systems invariant under a symmetry group both in the continuous and discrete cases. This provides an explicit conservation law (first integral) given by a closed formula which can be algorithmically implemented. In the discrete case, the conservation law is moreover computable in a finite number of steps.