Shaykh Muhammad ibn Saalih al-Uthaymeen rahimahullaah in his Majmoo’ Fataawaa vol. 20, pages 42-43 was asked:
Q: Is it permissible to fast the day of Aashooraa by itself – without fasting a day before it or after it; because I read in a journal of religious verdicts that such is allowed – due to the fact that the Jews do not fast it (the day of Aashooraa) nowadays?
A: Singling out Aashooraa (10th of Muharram) with fasting is not a matter that the people of knowledge have agreed upon; so from them are those that do not see singling it out with fasting as being disliked.
However what is better is that one fasts a day before it or a day after it; and fasting the ninth is better than fasting the eleventh, meaning: it is better to fast a day before it due to the saying of the Prophet sallAllaahu `alaihi wa sallam: “If I live until the next year I will certainly fast the ninth. [Reported by Muslim no. 1134] i.e. along with the tenth.
And some of the people of knowledge have mentioned that fasting the day of Aashooraa is of three types:
(i) That one fasts a day before it or a day after it.
(ii) That one singles it out with fasting.
(iii) That one fasts a day before it and a day after it.
And they mention that which is best is that one fasts a day before it and a day after it, then (the second best) is to fast the ninth day with the tenth day, then (the third best) is to fast the tenth day with the eleventh day, then (the fourth best) is to single it out with fasting.
And what is apparent is that singling it out with fasting is not disliked, however it is better that he combines it with the day before or the day after.