Sheikh Muhammad b. Sâlih al-`Uthaymîn
Voluntary acts of worship are of two kinds: those that have a specific cause for them and those that do not. Those voluntary acts of worship that have a specific cause for them should not be made up if that cause is missed.
For instance, there is the prayer of greeting the mosque (tahiyyah al-masjid). If a man enters the mosque and sits down for a decent amount of time and then decides to get up and offer this prayer, the prayer that he offers will not be considered tahiyyah al-masjid. The reason for this is that tahiyyah al-masjid is a prayer that is connected with a specific cause – in this case entering the mosque.
It appears that the same can be said for the fast of `Arafah and the fast of `Ashûrâ. Therefore, if a person delays one of these fasts without any excuse for doing so, then it is without doubt that he will not be able to make it up. If he does attempt to make it up, he will not get the special benefits conferred upon one who observes one of those two special fasts.
In a case where a person has an excuse that prevents him from fasting – like a person who is sick or a woman who is menstruating on that particular day – then it still appears that the fast should not be made up. Those fasts are particular for those two specific days, and they cannot be offered if that day is missed.
Source: Islam Today