Question:
Which are the days where fasting is obligatory in Muharram?
Answer:
All perfect praise be to Allah, the Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His Slave and Messenger.
It is not obligatory to fast the month of Muharram or any day of it. Scholars hold various opinions regarding fasting the tenth day of Muharram with regard to whether it was obligatory before the fasting in Ramadan became obligatory or not, and there are two opinions regarding this issue; however, after fasting in Ramadan became obligatory, fasting the tenth day of Muharram became merely favorable (i.e., recommended). Imaam Ash-Shawkaani said, "Ibn ‘Abdul-Barr reported a consensus of the scholars regarding the non-obligation of fasting the tenth of Muharram and of the fact that it is favorable (i.e., recommended) to fast it."
One of the proofs that it is recommended to fast voluntarily in Muharram is that the Prophet said: "The best fasting after Ramadan is the fasting of Muharram and the best prayer after the obligatory prayer is the night voluntary prayer." [Muslim, Abu Daawood, An-Nasaa’i, Ibn Maajah and At-Tirmithi]
It is favorable to fast the tenth of Muharram along with the ninth or to fast the tenth of Muharram along with one day before it and one day after it, or to fast it along with a day after it in order to differ from the Jews (who only fast that day). However, it is sufficient to fast on the tenth of Muharram alone.
Allah Knows best.