The actual industrial processes are always accompanies by many non-Gaussian behaviors due to the systems complexity. These behaviors are fractional order characteristics, which are very difficult to analyze by traditional analysis methods. This paper presents a detail fractional order theory analyses based on the fractional order characteristics present in industrial process. Initially, the -stable distribution is employed to fit the probability density distribution of the data and the auto correlation function is applied to find the long range dependence characteristic hidden in the process. Next, a re-scaled range method and multifractal detrended fluctuation analysis method is applied to analyze the fractional order features of the process in detail. Then, a fractional auto-regressive integrated moving average model (FARIMA) is proposed to predict accurately of the time series based on the fractional order characteristic of the system. Experimental results show that the superiority for prediction model with fractional order thinking.