MD11 Captain reported APU fire alert warning resulted in a divert.

Narrative

Preflight walk around and interior checks were completed with no discrepancies. APU FIRE Level 3 alert; master warning illuminated; the APU fire aural warning sounded and APU Fire indication in the APU Fire handle illuminated near ZZZ VOR at FL350 cruising at .85M. Confirmed indications with the FO (First Officer) and performed the phase 1 by pulling and rotating the APU Fire handle to discharge the agent. When the indications did not subside; we confirmed and rotated the handle to discharge the second agent. The indications remained; then we ran the QRH to confirm the phase 1 procedure and complete any remaining items. It was the FO's leg and was Pilot Flying and I was Pilot Monitoring; aircraft control was transferred and I became the Pilot Flying. The indications remained during the remainder of the flight. We requested priority handling and turned toward ZZZ1. We requested Fire assistance at ZZZ1 and proceeded direct in an [expedited] descent. All indications remained; we proceeded direct to ZZZ1 for a visual approach to Runway XXL; stopped on the runway and shutdown engines 2 & 3; and began the evacuation procedures; the Fire Chief and Operation Manager then notified us through Tower there were no visual indications of a fire. The APU Fire indication subsided upon landing. We then determined it was safe to taxi the aircraft to Company parking. Upon shutdown and post flight inspections we discovered the APU door was fully open. No other pertinent items to report.Cause - Equipment malfunction of the APU Fire detection system.Suggestion - Thorough maintenance inspections and routine equipment operational checks.