Is one who sighted the new moon alone, and whose testimony was not accepted, obligated to fast or break the fast alone?

The correct view is that a Muslim should fast and break fast with the people, due to the Prophet's (peace and blessings be upon him) saying: "Fasting is the day you fast, and breaking fast is the day you break fast," unless he is alone in the wilderness, in which case he acts according to his own sighting.