What should the questioner do regarding his wife and children who do not pray Fajr on time due to late-night studying and work, and is he accountable for this according to the Hadith: "Each of you is a shepherd and each of you is responsible for his flock"?

The questioner must order his wife and children to maintain prayer at its appointed time, and remind them of Allah's punishment for those who neglect it, citing Quranic verses that command Muslims and their families to pray, such as the Almighty's saying: {O you who have believed, protect yourselves and your families from a Fire} [At-Tahrim: 6], and His saying: {And enjoin prayer upon your family} [Taha: 132]. He should wake them for prayer before its time expires, especially the children. The Sharia has commanded striking children for abandoning prayer if they reach the age of ten. If the reason for missing prayer is late sleep, then he must order them to sleep early, because staying up late is disliked. If the father exerts his effort in advising, guiding, and disciplining, then he has fulfilled his duty, and he must continue to supplicate for their guidance.