By providing the generalisation of integration and differentiation, and incorporating the memory and hereditary effects, fractional-order modelling has gotten significant attention in the past few years. One of the extensively studied and utilised models to describe the glucose-insulin system of a human body is Bergman's minimal model. This non-linear model comprises of integer-order differential equations. However, comparison with the experimental data shows that the fractional-order version of Bergman's minimal model is a better representative of the glucose-insulin system than its original integer-order model. To design a control law for an artificial pancreas for a diabetic patient using a fractional-order model, different techniques, including feedback linearisation, have been applied in the literature. The authors' previous work shows that the fractional-order version of Bergman's model describes the glucose-insulin system in a better way than the integer-order model. This study applies the sliding mode control technique and then compares the obtained simulation results with the ones obtained using feedback linearisation.