Praise be to Allah.
Is sleeping after Fajr haram?
As far as a person’s sleeping after praying Fajr is concerned, no text (of Quran or hadith) has been reported to indicate that this is prohibited, so the general principle applies (i.e., everything is permitted except that which has been expressly forbidden).
But the practice of the Prophet (peace and blessings of Allah be upon him) and his Companions after praying Fajr was to remain sitting in the place where they had prayed until the sun rose, as is reported in Sahih Muslim (1/463) in the hadith of Sammak ibn Harb, who said: “I asked Jabir ibn Samurah, ‘Did you used to sit with the Messenger of Allah?’ He said, ‘Yes, frequently. He would not get up from the place where he had prayed Subh until the sun rose. When the sun rose, he would get up. They used to talk about things that had happened during the Jahiliyyah, and they would laugh and smile.’”
Also, the Prophet (peace and blessings of Allah be upon him) asked his Lord to bless his ummah in the mornings, as is reported in the hadith of Sakhr al-Ghamidi, who said: “The Messenger of Allah (peace and blessings of Allah be upon him) said: “O Allah, bless my ummah in the mornings.’ Whenever he sent out troops or an army, he would send them at the beginning of the day.’” Sakhr was a trader, and he used to send out his caravans at the beginning of the day, and he did well as a result and made money.” (Reported by Abu Dawud, al-Tirmidhi and Ibn Majah, with an isnad in which there is some jahalah (i.e., one narrator is unknown); corroborating evidence is to be found in a hadith narrated by ‘Ali, Ibn ‘Umar, Ibn 'Abbas, Ibn Mas’ud and others, may Allah be pleased with them all.)
For this reason some of the salaf disliked the idea of sleeping after Fajr. Ibn Abi Shaybah reported in his
Musannaf (5/222, no. 25442) with a sahih isnad from ‘Urwah ibn al-Zubayr that he said: “Al-Zubayr used to forbid his children to sleep in the morning.” ‘Urwah said: “I do not hear of any man who sleeps in the morning, but I lose interest in that person.”
In summary then, people should make the most of this time which can bring many benefits in this world and in the Hereafter, but if a person sleeps at this time to gain strength to do his work, there is nothing wrong with this, especially if it is not easy for him to sleep at any other time of the day.
Ibn Abi Shaybah reported in his Musannaf (5/223, no. 25454) from the hadith of Abu Yazid al-Madini who said: “Umar came to Suhayb one morning and found him sleeping, so he sat down until he woke up. Suhayb said: ‘The Amir al-Muminin is sitting in his place and Suhayb is sleeping!’ ‘Umar said to him: ‘I did not like to disturb your sleep that could be beneficial for you.’”
Is sleeping after ‘Asr makruh?
As for sleeping after ‘Asr , this is also permitted; there is no sahih hadith from the Prophet (peace and blessings of Allah be upon him) to indicate that sleeping at this time is prohibited.
As for the words, “Whoever sleeps after ‘Asr and loses his mind as a result has no-one to blame but himself,” which are attributed to the Prophet (peace and blessings of Allah be upon him), this is a false hadith and there is no proof that these words were uttered by the Prophet (peace and blessings of Allah be upon him). (See: Silsilat al-Da’ifah, no. 39)
And Allah knows best.