Based on the stability theory of fractional ordinary differential equations,the fractional dynamics of the newly proposed Lü chaotic system was analyzed.The range of order parameter was given by judging the stability of the equilibrium of the locally linearized system and by using bifurcation graph analysis.Furthermore,a synchronization observer was designed for linear generalized synchronization of such a newly proposed nonlinear chaotic system,which has the dynamic behavior of realizing arbitrary linear generalized synchronization including classical complete synchronization,anti-synchronization,projective synchronization as special cases with the original system.Finally,the numerical simulation verifies our results.