Is there any religious obligation about fasting in the days of the holy nights?
The Prophet Muhammad (saw) said, “When it is the night of the middle of Sha’ban, spend its night in prayer and observe a fast on that day. For Allah descends at sunset on that night to the lowest heaven and says: ‘Is there no one who will ask Me for forgiveness, that I may forgive him? Is there no one who will ask Me for provision, that I may provide for him? Is there no one who is afflicted by trouble, that I may relieve him?’ And so on, until dawn comes.” (See. Tirmidhi, Sawm, 39; Ibn Majah, Iqamat al- Salat, 191). On the other hand, the Prophet (saw) would fast on the first nine days of Dhu al-Hijjah, on Mondays and Thursdays, on the days of Ashura and Arafah (Muslim, Siyam, 196, 197; Ibn Majah, Siyam, 41,42) and replied people who asked about fasting on Mondays as, “It is (the day) when I was born and revelation was sent down to me.” (Muslim, Siyam, 198)
Based on this and similar hadiths, some Islamic scholars said that it is mustahab for the other days and nights which are considered as virtuous to be revived with acts of worship.
Source: Presidency Of Religious Affairs The Turkey, High Board of Religious Affairs FATWAS