  Using the fact that extremum of variation of generalized action can lead to
the fractional dynamics in the case of systems with long-range interaction and
long-term memory function, we consider two different applications of the action
principle: generalized Noether's theorem and Hamiltonian type equations. In the
first case, we derive conservation laws in the form of continuity equations
that consist of fractional time-space derivatives. Among applications of these
results, we consider a chain of coupled oscillators with a power-wise memory
function and power-wise interaction between oscillators. In the second case, we
consider an example of fractional differential action 1-form and find the
corresponding Hamiltonian type equations from the closed condition of the form.
