At about 1553 Alaska time, a Piper PA-31-350 was damaged during an inadvertent wheels-up landing at Fairbanks International Airport. The pilot and eight passengers aboard the Part 135 flight were not injured. The pilot said that, as he entered the pattern, he was told by the tower to cross over and enter right traffic for runway 1. The tower then told him he would have to extend downwind because of traffic. The pilot said he decided not to put the landing gear down at the usual point because of the request to extend his pattern. He said as he started to extend his pattern, the tower asked him to expedite a base turn and keep it tight. The pilot said he failed to complete his checklist on the base leg and, on final, airplane behind him said they were too close and they were going to go around. In the confusion, he said he never completed his before-landing checklist and landed the airplane with the gear retracted. The pilot said fatigue added to his confusion.