It is Likable to Fast on the Day of Ashura
The day of Ashura is the 10th of the month of Muharram and fasting on it is likable as told by the Prophet(PBUH) who said: "Fasting the day of Ashura is an expiation for the preceding year."{Related by An`nassai`}.
In order for a person to receive the full reward from Almighty Allah, it is better that he/she fasts the 9th, 10th, and the 11th of Muharam, as stated by a number of scholars such as Ash-shafii` and others. If that wasn't possible, then he can fast Ashura with the day that comes before, or after it; however, if he fasted only on the day of Ashura, then it is permissible. Al-Imam An-nawawi(May Allah have mercy on him) stated: "The day of Ashura is the 10th of Muharam, and it is likable for a person to fast the 9th of Muharam as well."{Rawdat At-Talibeen}.
Al-khateeb Ash-shirbini said, " It is likable for a Muslim to fast on the 9th and 10th of Muharram to be on the safe side."{Moghni Al-Mohtaj}.