What is the ruling on ablution (wudu') and prayer for someone who suffers from continuous gas due to irritable bowel syndrome (IBS) and cannot control it? And is he required to offer expiation for an oath (kaffarat yamin) if he breaks his oath, repeatedly sworn, not to repeat ablution?

If flatulence is frequent to the extent that it's uncontrollable, and you don't find time for purification, then perform ablution after the prayer time begins and pray. Your ablution will not be invalidated. However, if you find time for purification, then wait, perform ablution, and pray, even if you miss the congregational prayer. If you suffer from obsessive thoughts (waswasah), disregard them and pay them no mind. The oaths you took under the influence of waswasah are not binding upon you.