Q: What do I do if I woke up after the adhan of Fajr and found out it was Ramadan?
A: Fasting is obliged upon everyone with the sighting of the new moon, regardless of the location, or, as a precautionary measure, when atmospheric conditions prevent a potential sighting on the 29th of Shaban. If a positive sighting is confirmed during the day and you did not make the intention to fast, you are to fast the remainder of the day and make up the day after Ramadan. Source: Sharh al-Muntaha
This answer was collected from HanbaliDisciples.com. The questions have been answered by Imam John Starling.