Is fasting on the first day of the Hijri year (1st of Muharram) sunnah?

It has not been established that fasting the first day of Muharram is a Sunnah in itself. Rather, the Sunnah is to fast frequently during the month of Muharram in general, based on the Prophet's (peace be upon him) saying: "The best fasting after Ramadan is Allah's month of Muharram." Similarly, encouragement for fasting the tenth day of it has been established.