What Is the Ruling on Singling out 'Ashura for Fasting?
Question

Is it permissible to fast 'Ashura only without fasting the day before or the day after?
Praise be to Allah.Shaykh al-Islam [Ibn Taymiyah] said: Fasting the day of 'Ashura is expiation for one year, and it is not makrooh to single out this day for fasting. Al-Fataawa al-Kubra, part 5. 
In Tuhfat al-Muhtaaj by Ibn Hajar al-Haythami it says: There is nothing wrong with fasting 'Ashura on its own. Part 3, Baab Sawm al-Tatawwu’. 
The Standing Committee was asked this question and replied as follows: 
It is permissible to fast the day of 'Ashura on its own, but it is better to fast the day before it or the day after it. This is the Sunnah that is proven from the Prophet (peace and blessings of Allah be upon him), as he said, “If I am still alive next year, I will certainly fast the ninth.” Narrated by Muslim, 1134. 
Ibn ‘Abbaas (may Allah be pleased with him) said: He meant, along with the tenth. 
And Allah is the Source of strength.  
Al-Lajnah al-Daa’imah li’l-Buhooth al-‘Ilmiyyah wa’l-Ifta’, 11/401.
For more information, see the answers to questions No. (21775 ) and (303756 ).