Salamun Alaikum Sister,
There is no prescription in the Quran to fast on such a day or for the commemoration of any event. These are all additional concepts introduced into the name of religion for which the Quran gives no authority. The Quran clearly informs believers that fasting has been prescribed in the month of Ramadan (2:185). Furthermore, some expiations may also involve fasting (2:196; 4:92; 5:89; 5:95; 58:4). However, any fasts done for the sake of God should be encouraged (19:26) but this should not be considered as 'prescriptive' (obligatory).
I hope this helps,
Joseph.