The Sunnah of Prophet Muhammad (peace and blessings be upon him) aim at guiding people and bringing them closer to their Lord. In the Qur’an, Almighty Allah says,
(If you obey him [the Messenger of Allah], you are on the right way.) (An-Nur, 24:25)
true Muslims should avail themselves of the merit of every act of worship, especially those acts that Allah has granted great reward, such as fasting on the White Days, the Day of `Ashura’, and the Day of `Arafah.
Answering this question, Dr. Rajab Abu Maleeh, he said:
According to numerous hadiths, it is recommendable to fast on the White Days of each Hijri month. It is reported that the Prophet (peace and blessings be upon him) said, “[For] whoever fasts on three days of every month [the 13th, 14th, and 15th of every lunar month], it will be as if they have fasted for the entire year.”
therefore, the Prophet commanded his Companions to observe the fast on the White Days, asserting that this is regarded as fasting for an entire year.
However, those who are used to fasting on these days should not fast on the 13th of Dhul-Hijjah because this day is one of the Tashreeq Days during which fasting is forbidden. It is reported in Sahih Muslim (authentic book of Muslim) that the Prophet (peace and blessings be upon him) said, “The days of Mina are days of eating and drinking [lawful drinks] and remembering Allah.”
the more acceptable view is that of the Shafi`is, who opine that it is desirable to fast on the 16th of Dhul-Hijjah instead of the 13th day. This applies to those who are used to fasting on these days.
Apart from the fast of Ramadan, fasting is basically a recommended act of worship; it is not an obligation. Asserting this ruling, Imam Malik deemed it disliked to fast on these days (the 13th, 14th, and 15th of lunar months) when there is fear that people may think that this fasting is obligatory. So, he would rather fast on the 1st, 11th, and 21st of the lunar month.
The Prophet (peace and blessings be upon him) would neither regularly observe nor totally abandon the supererogatory acts of worship. Imam Muslim reported that `A’ishah (may Allah be pleased with her) said, “The Prophet (peace and blessings be upon him) used to fast for so long that we thought he would never stop fasting, and he would go without fasting for so long that we thought he would never fast again. I never saw the Messenger of Allah (peace and blessings be upon him) fast for a complete month, except for Ramadan.”
Also, Al-Bukhari reported that Anas (may Allah be pleased with him) said, “One would never wish to see him [the Prophet] pray at night except that he would really be doing so, or to see him asleep except that he would really be [asleep].”
He, the Prophet, would always perform acts of worship according to what was revealed to him through the light of prophethood of duties in their assigned times.