This paper presents the design and application of fractional single-input-single-output (SISO) controllers to a grinding mill circuit, which is a multiple-input-multiple-output (MIMO) process. Two kinds of controllers are presented: fractional order proportional-integral (FOPI) controllers, and a combination of FOPI and fractional order model reference adaptive controllers (FOMRAC). The parameters of the controller are tuned using off-line particle swarm optimization. In the presence of disturbances and process noise, the SISO fractional controllers achieve similar or better performance compared to linear model predictive control (LMPC). (C) 2017 Elsevier Ltd. All rights reserved.