The generalized Lagrangian is defined in a dissipative electromagnetic medium on the basis of the combination of dynamical analysis and fractional derivative.Lorentz medium models are obtained by formulating relevant EulerLagrange equations.The invariance is obtained subsequently by investigating the invariance of time variation in the system,and then the relation between the related Hamiltonian and electromagnetic energy density is investigated.Canonical equations are obtained eventually.The electrodynamic interpretation on dissipative electromagnetic systems is revesled.