This work presents a fractional order Proportional Integral and Derivative controller with adaptation characteristics in the control parameters depending on the required output, gain scheduling fractional order PID (GS-FO-PID). The fractional order PID is applied to the voltage control of a DC–DC buck quadratic converter (QBC). The DC–DC buck quadratic converter is designed to operate at 12 V, although in the simulation tests, the output voltage ranges from 5 to 36 V. The performance of the GS-FO-PID is compared with the one from a classic PID. The GS-FO-PID presents better performance when the reference voltage is changed. In the same way, the behavior of the converter with the reference fixed to 12 V output is analyzed with load changes; for this case, the amplitude value of the ripple when the converter is driven by the GS-FO-PID almost has no variation.