This is a review article which elaborates the results presented in \cite{Noether_MJ_TMA_SP}, where the variational principle of Herglotz type with a Lagrangian that depends on fractional derivatives of both real and complex orders is formulated and the invariance of this principle under the action of a local group of symmetries is determined. The conservation law for the corresponding fractional Euler Lagrange equation is obtained and a sequence of approximations of a fractional Euler--Lagrange equation by systems of integer order equations established and analyzed.