The Prophet (peace and blessings be upon him) has exhorted us to fast during certain days: six days of Shawwal, the first ten days of the month of Dhul-Hijjah, especially the day of `Arafah for those who are not performing Hajj, fasting Mondays and Thursdays, fasting three days (the 13th , 14th, and 15th) of every month.
As for fasting Mondays and Thursdays, Abu Hurayrah (may Allah be pleased with him) reported that the Prophet (peace and blessings be upon him) used to fast on Monday and Thursday. On being asked about that the Prophet said: “Deeds are presented on every Monday and Thursday. Allah forgives every Muslim or every believer, except for those who are forsaking each other. He says [about them]: ‘Leave them.’ “ (Reported by Ahmad with authentic chain of narrators)
It is recorded in Sahih Muslim that the Prophet (peace and blessings be upon him) when asked about fasting on Monday, said: “That is the day on which I was born and the day on which I received revelation.” As for fasting the 13th , 14th, and 15th of each month, Abu Dharr Al-Ghafari reported: “The Messenger of Allah ordered us to fast for three days of every month – that is, on the days of the full moon (the 13th, 14th, and 15th of the lunar month). And he said: ‘It is like fasting the whole year.’” (Reported by An-Nasa’i)
It’s now clear that observing fasting on those days moves in line with the practice of the noble Prophet (peace and blessings be upon him) who set a shinning example for Muslims to follow, in compliance with Allah’s words: ” Ye have indeed in the Messenger of Allah a beautiful pattern (of conduct) for any one whose hope is in Allah and the Final Day, and who engages much in the Praise of Allah.” (Al-Ahzab: 21)