Is it possible to fast al-ayyaam al-beed based on the dates published in newspapers or calendars?

Al-ayyaam al-beed are the thirteenth, fourteenth and
fifteenth of every hijri month. A hadeeth concerning them was narrated by
Abu Dharr (may Allah be pleased with him) who said: The Messenger of Allah
(blessings and peace of Allah be upon him) said to me: “If you fast any day
of the month, then fast on the thirteenth, fourteenth and fifteenth.”
Narrated by at-Tirmidhi (761) and an-Nasaa’i (2424); classed as saheeh by
al-Albaani in Saheeh at-Targheeb (1038). 

The beginning of the month is known from sighting of the new
moon. If it is possible to ask those who are involved in moon-sighting at
the beginning of each month, then that is good. Or you can rely on the moon
sighting in some countries which announce it every month. Otherwise, one may
fast on the basis of calendars, as it is acceptable to base one’s actions on
what is most likely to be the case. 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked:

It is no secret that people are not aware of the beginning of
the ordinary months, so what is the situation with regard to fasting
al-ayyaam al-beed every month? What I mean is: how can a person know when
these days are so that he may fast at that time? I hope that you can advise
us, may Allah reward you with good. 

He replied: It is allowed to fast on those days according to
calendars, acting on what appears most likely to be the case. If he observes
this fast on other days, that is acceptable, because the Prophet (blessings
and peace of Allah be upon him) encouraged doing these fasts in every month,
but he did not limit it to al-ayaam al-beed, as it is narrated in
as-Saheehayn from the Messenger of Allah (blessings and peace of Allah
be upon him) that he said to ‘Abdullah ibn ‘Amr ibn al-‘Aas (may Allah be
pleased with him): “Fast three days of every month, for a good deed brings a
tenfold reward, and that will be like fasting for a lifetime.” In
as-Saheehayn it is narrated that Abu Hurayrah (may Allah be pleased with
him) said: The Messenger of Allah (blessings and peace of Allah be upon him)
advised me to do three things: to fast three days of every month, to offer
two rak‘ahs of Duha prayer, and to pray Witr before sleeping. And there are
many hadeeths concerning this matter. The individual has the choice: if he
wishes he may do them together (consecutively), or if he wishes he may
separate them, because the hadeeths are general in meaning and do not
specify that these fasts must be done consecutively. And Allah is the source
of strength.

End quote from Majmoo‘ Fataawa Ibn Baaz (15/282) 

If we assume that we were mistaken about one of these days,
that does not matter; rather there is the hope that the one who fasts will
be granted the reward in full, because he has an excuse and he did what he
was able to. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
Fasting three days of every month is Sunnah. The Prophet (blessings and
peace of Allah be upon him) said that fasting three days of every month is
like fasting for an entire lifetime. But it is preferable to do that on the
ayaam al-beed: the thirteenth, fourteenth and fifteenth of the month. If
that is not possible because a woman has her period, or because the
individual is travelling or has a guest or gets tired or is sick, and the
like, then the reward may also be obtained by the one who fasts days others
than these three. ‘Aa’ishah (may Allah be pleased with her) said: The
Prophet (blessings and peace of Allah be upon him) used to fast on three
days of every month and he would not mind whether he fasted them at the
beginning of the month, or in the middle, or at the end. So this matter is
broad in scope. Fasting three days of every month is Sunnah, whether that is
at the beginning of the month or in the middle or at the end. But if it is
during the three ayaam al-beed, that is preferable. But if he was unable to
fast because of some reason or need, then we hope that Allah, may He be
exalted, will decree reward for everyone who has the habit of fasting these
days, but is not able to do so because there was some reason for that.

End quote from Fataawa Noor ‘ala ad-Darb. 

With regard to our website, the date on it is based on
calendars, except in the case of Ramadan and Dhu’l-Hijjah. 

And Allah knows best.