Citation jet pilot reported receiving a low altitude alert from ATC during approach. Pilot climbed and continued approach.

Narrative

Initial descent to vectors for GPS RWY XX was steep. Pilot slightly behind the airplane. on heading 120/6000' for vectors to final; Pro-line 21 FSU failed; lost chart depiction of approach. FSU had been intermittent; pilot didn't have iPad chart ready; fumbled for paper chart backup and getting lighting on the chart. turn to intercept final @ 270 degrees. turn to heading 240/descend to 5;300' cleared for the approach. pilot read back 240/3;500'. consumed time asked for clarification on the heading which didn't seem correct. should have recognized when read back that 3;500' was wrong (field elevation is ~3;600'). controller advised low altitude alert; climb. Field in sight confirmed; cleared for the visual approach.Observations:behind the airplane; starting with the descent to 6;000.FSU failed; should have asked for time to sort out paper or iPad copy of chart.Should have recognized when 3;500' read back (heard myself saying it) that it was an incorrect altitude.Should have not commenced the descent and then asked about the 240 heading. Should have stayed at 6;000' and cleared up both heading and altitude assignment.Fatigue could have been a factor. I started the day at ZZZ1; approximately 2;000 nm away. It was XO15 local time after starting the day at XA00.Classic error chain.