Is the intention to fast an obligatory fast valid if it occurs after Fajr?

The majority of scholars stipulated the intention (niyyah) as a condition for the validity of fasting, whether it be obligatory or supererogatory. However, Zufar from the Hanafis did not consider intention a condition for the Ramadan fast, except for the sick and the traveler.

As for forming the intention the night before (tabyīt al-niyyah): - The Hanafis permitted delaying the intention for the Ramadan fast, specified vows, and supererogatory fasts until the great forenoon (al-ḍaḥwat al-kubrā), but they obligated forming the intention the night before in cases other than these. - The Malikis stipulated that the intention must precede dawn for all types of fasting, except for the Day of Ashura. - The Shafi'is and Hanbalis differentiated between obligatory and supererogatory fasts. They obligated forming the intention the night before for obligatory fasts, and permitted forming the intention for supererogatory fasts before or slightly after zawāl (midday).