EMB-505 Captain reported an engine failure during initial climb from a tower controlled airport; during daylight conditions. The aircraft returned to the departure airport and landed safely.

Narrative

Right engine fail during initial climb Runway XR ZZZ. Approx 2000 ft. MSL/180KTS; gear and flaps retracted two loud bangs were heard along with airframe shudder; N1 gage indicated right engine fail; 3 more loud bangs heard and engine began to roll back along with yaw. With the aircraft under positive control [priority handling requested] with request to return back to ZZZ. Request was granted; Runway XR was offered for visual approach and landing which we accepted. Inflight engine shutdown QRC; engine inop approach QRC; and engine inop landing QRC completed.Approach and landing were uneventful except normal braking was initially available but became ineffective; braking was used to stop the aircraft on Taxiway 1 (ATC request). There was ample room for vehicles to access the area around the aircraft. I requested personnel to inspect the aircraft for fire of which there was no evidence from the outside nor from the cockpit. With aircraft secure and shutdown I requested transport for the passenger and First Officer back to FBO which they accommodated. I stayed on the aircraft during tow and until secure in the FBO hangar.We could have taken a little more time during the approach phase for example; longer down wind.