Skyhawk 172/Cutlass 172
Air Traffic Control Fully Certified
Situational Awareness; Communication Breakdown; Fatigue
ATC Issue All Types; Airspace Violation All Types; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance
Staffing; Human Factors
I was working the GC; CD and CIC positions combined.  Aircraft X called for IFR clearance to ZZZ.  I didn't realize that he was calling from ZZZ1 and believed him to be on the ground at ZZZ2.  Because I believed the aircraft to be at ZZZ1 I did not issue a hold for release to the aircraft.  Aircraft X subsequently departed ZZZ2 without authorization from the approach control.This was my sixth day working and frankly I was tired and just missed it.  This was the third week in a row that I have been working six days a week.  I am scheduled to work two more weeks of six day work weeks prior to some vacation time.  I believe that fatigue was a major factor and the only cure for this will be an elimination of the amount of overtime we have been working.  However; we have been working six day work weeks since April of 2008 and there does not seem to be an end in sight.
Controller working combined positions issues IFR clearance to an aircraft on the ground at a nearby airport; believing the aircraft to be on the ground at the airport where the tower is located.