Molecular dynamics simulation (MDS) is adopted to investigate the characteristic of fractional motion of molecules in liquid phase, vapor phase and liquid-vapor interface in the paper. Based on the theory of mean free path and Shannon sampling theorem, the way to determine a universal criterion of time step of simulation is presented. It is shown that there exists difference in the regular pattern of molecular motion in the state of liquid and vapor phase. The fractional features are different for different matter states. Under the condition of same temperature, the characteristic fractional number of molecular motion in liquid state is greater than one in vapor state. It is shown that the fractional dimension numbers in the X, Y and Z direction of the liquid-vapor interface are different. This proves that the liquid-vapor interface has anisotropic character.

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