Is it allowed to fast on Monday without fasting Thursday of the same week or fast on Thursday without fasting the Monday of the same week?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Fasting Monday and Thursday every week is a recommended Sunnah. It is firmly established from the Prophet of Allaah, sallallaahu ‘alayhi wa sallam, that he used to fast Monday and Thursday. When asked about that, he said: “The deeds of people are lifted (to Allaah) on Monday and Thursday.” [Abu Daawood]

However, fasting them together is not obligatory, i.e. the one who fasts Monday does not have to fast Thursday and vice versa. It is permissible to fast one and to not fast the other. For more information, please refer to Fatwa 114626.

Allaah Knows best.