Fasting, according to the prescription of Allah, is of two kinds:
1- Compulsory
Fasting
This is also of two kinds:
a-Obligatory fasting which, from the beginning,
Allah Almighty decreed as an obligation upon His servants. This is Fasting in the month of Ramadan, one of the five pillars of Islam.
b-Obligatory fasting whose compulsion was due to or caused by the servant of Allah. Examples include fasting due to pledges or as a result of expiation for one’s inequities.
2- Recommended Fasting
This includes all forms of Fasting recommended by Allah Almighty and/or His Messenger. Examples of this is fasting on Mondays and Thursdays, three days of every lunar month, on the tenth day of Muharram (first month of the Islamic calendar), the first ten days of Dhul Hijjah (the 12th month) and on the Day of ‘Arafah (i.e. the 9th day of Dhul Hijjah).
source:
islamkingdom