Air carrier Captain reported an engine caught fire after parking at the gate. There was no fire indication message but aircraft status page displayed a Eng Fuel Value R.

Narrative

After parking at the gate; delayed flight arriving into ZZZ; normal shut down and parking checklist completed. After door 2L opened; ground crew noticed excessive smoke and brief fire on the right engine; after shut down. There were no cockpit fire indications. After debriefing with the few crew members that remained onboard; Gate Agent made announcement to passengers; exit the plane immediately and leave all luggage behind. I did not execute an evacuation or had any knowledge of the Gate Agent announcement. The F/O and I; opened our cockpit windows; from CA side- trying to get more information from a ground crew person; and the F/O looking back at the right engine. I called ops freq and advised ZZZ Ops of the situation. Fire department was called by ground crew. I then walked to the cabin; with the remaining passengers exiting. The Purser and several F/A's had left the aircraft. The Purser did NOT communicate with me nor the F/O...unsatisfactory! The remaining F/A's assisted the Gate Agent; the F/O; and myself- to walk the passenger bags from the cabin to the gate; we finished a debrief and exited the plane at the gate. The aircraft status page then displayed a 'Eng Fuel Value R ' message on the status page. We also had mechanics in cockpit after the smoke/fire on the right engine asking if we had a fire light/indication. We had no fire indication.