About fractional Hamiltonian systems

We follow Stanislavsky's approach of Hamiltonian formalism for fractional systems, as a model problem for the study of chaotic Hamiltonian systems. We prove that his formalism can be retrieved from the fractional embedding theory. We deduce that the fractional Hamiltonian systems of Stanislavsky stem from a particular least action principle, said to be causal . In this case, the fractional embedding becomes coherent.