This paper deals with the fractional modelling of a DC-DC buck-boost converter, suitable in solarpowered electrical generation systems, and the design of a fractional controller for the aforementioned switching converter. Although the modelling and design of the controller is carried out for this particular DC-DC converter, it can be easily extended to other king of switching converter. In addition, the comparison between integer-order plant/controller and fractional-order plants/controller is carried out. The article also shows that, under the same design conditions, the fractional-order controller has a better performance and behaviour than with classical integer-order controller in both situations, that is, with integer-order plant and fractional-order plant models.