Beech 1900
Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Multiengine
Flight Crew Last 90 Days 100; Flight Crew Total 7800; Flight Crew Type 3000
Situational Awareness; Fatigue
Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance; Flight Crew Became Reoriented
Human Factors
I was respositioning my aircraft to a nearby airport after dropping off a crewmember. There was no specified airway or fixes because I was to be operating in Razorback's airspace the entire time.  I had just completed a recurrent checkride in the area and was familiar with the weather; airspace; and airports.On departure from Runway 34 at XNA; I climbed through 3000 on a heading of 339; then when switched to Razorback Approach I cancelled IFR in visual conditions to proceed to ZZZ. Having cancelled IFR I was already thinking ahead to navigating viusally. Razorback Departure instructed me to turn left to heading 200 for following traffic.  The unexpected instruction caught me off-guard and I asked them to confirm the LEFT turn to 200.  When they confirmed; I turned RIGHT in error; which pointed me back towards the airport. This brought me on a bearing towards a corporate jet that had just departed. I saw them leave the runway and began turning southeast away from the assigned heading when they called departure to report that I was causing a Resolution Advisory.I was instructed to turn to heading 090; and I complied while stating that I had the jet in sight; and that I had ZZZ in sight and requested to navigate visually. At this point I did not realize that I had turned the wrong way; and believed that ATC had given me a vector that had caused the RA.  Razorback Departure instructed me to maintain a 090 heading and shortly thereafter a supervisor came on and explained that I had turned the wrong way.  At all times; I was in VFR conditions; and as soon as I had the airport in sight I also saw the jet. I sincerely regret my error.  The error was mine and a contributing factor was my expectation of being given a particular instruction. ATC gave me a clear instruction; I read it back and even asked for confirmation; but I turned the way I expected to hear; rather than what was instructed and what I read back.  My focus was on quickly completing my reposition flight; whereas it should have been on the process of the flight.  Another factor was feeling tired; though not fatigued to a point that I thought would affect safety- I had just finished a recurrent ride and was returning to my normal duty station in preparation for the evening flight. Familarity with the area is also a factor- I knew where I was and where I wanted to go; and that contributed to what I expected to hear.In the future; maintaining an IFR flight plan and planning for an instrument approach rather than cancelling IFR to shorten a flight would reduce the chances of committing a similar error; as would taking better stock of my mental state and taking rest or calling for a replacement crew if I am not in good condition to fly.
B190 pilot reported an airborne conflict after turning the wrong direction in response to an ATC clearance. Fatigue was cited as a contributing factor.