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Degradation processes of practical chemical engineering systems are difficult to model accurately because of complicated nonlinearities, non‐stationarities, and non‐Markovian properties. Traditional prognostics techniques tend to neglect the multi‐mode switching issue, and therefore cannot be used for predicting the remaining useful life (RUL) of a piece of long‐life equipment, especially when it is continuously operated under varying modes. Specifically, the stationarity of differential data also plays an important role in depicting the evolutionary trend, and further affects the extrapolation procedure for RUL prediction. In this paper, we construct a multi‐mode degradation model with regard to fractional diffusion processes by considering both stationary and non‐stationary increments. The drift term is represented as a time‐related nonlinear function, while the diffusion term is driven by fractional Brownian motion (FBM) or sub‐fractional Brownian motion (sub‐FBM), according to the results of the stationary test. Based on the monitored data, the model is identified by combining change‐point detection and parameter estimation. The closed‐form distribution of RUL is then derived through a weak convergence transformation. A numerical example and a case study of a large blast furnace are provided to evaluate the performance of the proposed prognostics framework. [ABSTRACT FROM AUTHOR]