Fasting on the thirteenth, fourteenth and the fifteenth day of every lunar month is generously rewarded by Allah Almighty. It stands to reason that fasting these three days is worked out according to the lunar Islamic calendar.

Shedding more light on the issue, Sheikh Muhammad Saleh Al-Munajjid, the prominent Islamic scholar and author, states:

“The virtues of fasting are immense, and a number of authentic hadiths state this, such as the following:
The Prophet (peace and blessings be upon him) is reported to have said: “Whoever fasts one day for Allah’s sake, Allah will keep his face seventy years’ distance away from the Fire because of it.” (Sahih Muslim)

The Prophet (peace and blessings be upon him) is also reported to have said: “Whoever fasts a day seeking the pleasure of Allah and then dies (i.e., having the fasting as the last thing he does) will enter Paradise.” (Musnad Ahmad).

Abu Dharr Al-Ghifari reported: “The Messenger of Allah enjoined us to fast 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.” (An-Nas’i and Ibn Hibban)

Voluntary fasts will make up for any shortfall in obligatory fasts. Examples of voluntary fasts include `Ashura’, the Day of `Arafah, Mondays and Thursdays, six days of Shawwal, etc.

The timing of certain acts of worship is worked out according to the lunar months of Islamic calendar, not the solar months of the Western calendar. Allah Almighty says: “They ask you about the new moons. Say: These are signs to mark fixed periods of time for mankind and for the pilgrimage…” (Al-Baqarah: 189)”
In conclusion, we can say that the criterion through which the fasting of those days is observed is the Islamic lunar calendar.