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Recently, the fractional Noether's theorem derived by G. Frederico and D.F.M.Torres in Appl. Math. Comp. 217,3,2010 was proved to be wrong by R.A.C.Ferreira and A.B. Malinowska in JMAA 429, 2, 2015 using a counterexample anddoubts are stated about the validity of other Noether's type Theorem, inparticular(JMAA 334, 2007,Theorem 32). However, the counterexample does notexplain why and where the proof given in Appl. Math. Comp. 217,3,2010 does notwork. In this paper, we make a detailed analysis of the proof proposed by G.Frederico and D.F.M. Torres in JMAA 334, 2007 which is based on a fractionalgeneralization of a method proposed by J. Jost and X.Li-Jost in the classicalcase. This method is also used in Appl. Math. Comp. 217,3,2010. We first detailthis method and then its fractional version. Several points leading todifficulties are put in evidence, in particular the definition of variationalsymmetries and some properties of local group of transformations in thefractional case. These difficulties arise in several generalization of theJost's method, in particular in the discrete setting. We then derive afractional Noether's Theorem following this strategy, correcting the initialstatement of Frederico and Torres in JMAA 334, 2007 and obtaining analternative proof of the main result of Atanackovic and al. in NonlinearAnalysis 71, 2009.

About the Noether's theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof