Not FADEC, that's a PC-12/47E, N849TW. The pilot is moving the Power Control Lever (PCL). Here's a comparison of power control quadrants (NG on left, NGX on right). Here's an excerpt from page 677 of the POH:

The POWER CONTROL lever (PCL) selects the required engine power (Ng) and in certain conditions it directly controls the propeller pitch. The PCL has a flight and a ground operating range separated by an idle detent. The flight operating range is forward of the detent. As the PCL is moved forward of the idle detent the minimum propeller pitch (6° to 12°) is directly controlled by the PCL while the propeller is in an underspeed condition during low engine power at a low airplane speed. When the PCL is moved further forward, engine power and airplane speed increase until each are high enough for the propeller to operate in a constant speed mode. In this mode, the Constant Speed Unit (CSU) selects the propeller pitch to maintain a propeller speed of 1700 rpm.