In the Sufi tradition it is possible and advisable to fast during the three days of full moon (the day before, the day and the day after). The big daily fasting is happening though during the days of Ramadan.
How to fast?
It means do not eat, drink or smoke in the daylight, which means from the morning prayer to the evening prayer.
Days when the fasting is possible and advisable in
April: 14, 15, 16.
May: 13, 14, 15.
June: 12, 13, 14.
( for the details of the fasting see the article: The holy month of Ramadan)