FLC OF LTT FAILS TO CONTACT TWR PRIOR TO LNDG.

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ON A FLT FROM MEM-TUL. NAVED AROUND HVY TSTMS EARLIER IN NIGHT. PLTS FLYING LAST LEG OF A 3 DAY TRIP. ATC ASKED US TO RPT A B737 IN SIGHT FOR A VISUAL APCH TO RWY 36R AT TUL. WE HAD DIFFICULTY FINDING THE TFC DUE TO CITY LIGHTS IN BACKGROUND. WE FINALLY FOUND THE TFC AND RPTED IT 'IN SIGHT.' WE WERE TOLD TO FOLLOW THE B737 AND MAKE SHORT APCH. THERE WAS ANOTHER ACFT TO FOLLOW US. IN THE PROCESS WE WERE CLRED FOR THE VISUAL AND TOLD TO CONTACT THE TWR. WE WERE QUITE BUSY FINISHING CHKLISTS AND PREPARING FOR LNDG. WE BOTH FAILED TO FLIP THE RADIO OVER TO TWR AND RECEIVE AN AUDIBLE CLRNC TO LAND. ATC ASSUMED A 'LOST COM;' AND FLASHED US WITH A GREEN LIGHT. (NEITHER ONE OF US WERE LOOKING FOR IT THOUGH). AFTER CLRING THE RWY; WE NOTICED WE WERE STILL ON APCH FREQ; AND HAD NEVER CONTACTED THE TWR. WE RECEIVED CLRNC TO TAXI TO THE GATE; AFTER REESTABLISHING COMS WITH ATC. NO FURTHER INCIDENT. IN MY OPINION; CONTRIBUTING FACTORS WERE: 1) BEING HURRIED IN THE SHORT APCH CLRNC; AND 2) FATIGUE OF CREW. FLYING TIME IN LAST 5 DAYS; 14.8 HRS. DUTY TIME IN LAST 5 DAYS; 34 HRS. WE MADE A MISTAKE; BELIEVE ME WE ARE FULLY AWARE OF THIS FACT. THERE ARE NO EXCUSES FOR THIS AMONG A PROFESSIONAL FLC. HOWEVER; I WOULD SAY EMPHATICALLY 'SHAME ON THE FAA FOR EVEN CONSIDERING INCREASING FLT TIMES TO 10 HRS INSTEAD OF 8 BTWN REST;' AND 'SHAME ON THEM MORE FOR ALLOWING REDUCED REST AND DUTY TIMES OF EVEN 14 HRS.' WOULD YOU GET ON AN AIRPLANE IF YOU KNEW YOUR PLT GOT UP AT XA00 TO RPT FOR WORK AT XC30; AND IT WAS XR00 AT NIGHT?' HEY; IT'S LEGAL! BUT IT SHOULDN'T BE.