Over 99% of the baryonic matter in the universe is in the state of plasmas. Many phenomena observed in astrophysics and space physics are described by principles and laws of plasma. These phenomena include planetary formation, solar flares, star formation, solar and stellar winds, particle acceleration, black hole accretion and jet, Gamma ray bursts, supernova explosions, Galaxy formation and evolution, large-scale structure of the universe, etc. Compared with the integer order model, the fractional order equation can describe more precisely the historical dependence and long-range dependence of the hydrodynamic behavior based on the anomalous diffusion process in plasma. It is of great significance and prospect to apply the fractional order model to the field of plasma physics. The research status of the numerical solution of the fractional order model in plasma physics is reviewed, and the future development is also envisioned.