  We provide a general theoretical framework allowing us to extend the
classical Lie theory for partial differential equations to the case of
equations of fractional order. We propose a general prolongation formula for
the study of Lie symmetries in the case of an arbitrary finite number of
independent variables. We also prove the Lie theorem in the case of fractional
differential equations, showing that the proper space for the analysis of these
symmetries is the infinite dimensional jet space.
