Fasting in Rajab

Kharashah bin al-Hurr narrated: I saw Sayyiduna Umar bin al-Khattab (may Allah be pleased with him) striking people's hands over the fasts of Rajab until they put them into the food, and he would say: "Rajab! What is Rajab? Rajab is a month which the people of the Era of Ignorance used to venerate; when Islam came, it was abandoned."
Imam al-Tabarani recorded it in al-Mu'jam al-Awsat. Its chain contains a narrator, al-Hasan bin Jabalah; I have not found anyone who mentions him. Its remaining narrators are thiqat (trustworthy).

Abd al-Aziz bin Sa'id reports this statement from his father (the narrator Uthman says: his father had the honour of being a Companion); he narrated: The Prophet (peace and blessings be upon him) said: "Rajab is a great month in which Allah Almighty multiplies good deeds. Whoever fasts one day of Rajab, it is as though he fasted a whole year; whoever fasts seven days of it, the seven gates of Hell are closed for him; whoever fasts eight days of it, the eight gates of Paradise are opened for him; whoever fasts ten days, whatever he asks of Allah Almighty, Allah Almighty grants it to him; whoever fasts fifteen days, a caller calls out from the heaven saying: 'Your past sins have been forgiven, so begin your deeds anew.' And whoever does more (good), Allah Almighty also grants him more (reward). In the month of Rajab, Allah Almighty carried Sayyiduna Nuh (peace be upon him) in the Ark, so he fasted the month of Rajab and ordered his companions to fast as well." (Allamah al-Haythami says:) I say: After this he mentioned the full hadith; the complete report has already passed, along with the discussion of it, in the chapter on the fast of Ashura.

Sayyiduna Abu Hurayrah (may Allah be pleased with him) narrated: The Prophet (peace and blessings be upon him) did not fast a complete month after Ramadan, except for Rajab and Sha'ban.
Imam al-Tabarani recorded it in al-Mu'jam al-Awsat. Its chain contains a narrator, Yusuf bin Atiyyah al-Saffar, and he is da'if (weak).