  The concept of nonlinear self-adjointness is employed to construct the
conservation laws for fractional evolution equations using its Lie point
symmetries. The approach is demonstrated on subdiffusion and diffusion-wave
equations with the Riemann-Liouville and Caputo time-fractional derivatives. It
is shown that these equations are nonlinearly self-adjoint and therefore
desired conservation laws can be obtained using appropriate formal Lagrangians.
Fractional generalizations of the Noether operators are also proposed for the
equations with the Riemann-Liouville and Caputo time-fractional derivatives of
order $\alpha \in (0,2)$. Using these operators and formal Lagrangians, new
conserved vectors have been constructed for the linear and nonlinear fractional
subdiffusion and diffusion-wave equations corresponding to its Lie point
symmetries.
