'Aashooraa' fast is according to earlier lunar calendar
17-12-2013 | IslamWeb
Question:
In your article 'The Sacred Month of Moharrum' you have written that Messenger Musa (PBUH) celebrated his victory over Pharoah on the 10th of Muharrum (Ashoora). Whereas in another article on Hijri calendar u all have clearly stated that the Islamic calendar was started by Caliph Omar(RA). In the times of Messenger Moses (PBUH) there was no Islamic Calendar. So wherefrom did u get this information. It cannot be true for reasons given above. Please verify from history when u all narrate these true events.
Answer:
All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad 
is His slave and Messenger.
Allaah saved Prophet Moosa (Moses) 
and the Children of Israel on the day of ‘Aashooraa’ (i.e. 10th of Muharram); it is for this reason that the Jews (of the Prophet's time) fasted this day and we Muslims fast this day, as we are closer to Moosa than them, and in Islam, we are instructed to differ from them by fasting one day before ‘Aashooraa’ or one day after it.
Everything we mentioned is stated in the authentic Sunnah of the Prophet and we did not invent it. For instance, Ibn ‘Abbaas 
said, “When the Messenger of Allaah came to Madeenah, he found the Jews fasting the day of ‘Aashooraa’. They were asked about this and they said, ‘It is the day on which Allaah gave Moosa and the children of Israel victory over Pharaoh and we fast this day in honor of it.” Upon this the Prophet said: “We are worthier of Moosa,” and he commanded people to observe fasting on that day.” [Al-Bukhari]
In another narration, when the Prophet was told that the Jews fast this day, he said: “If I live until next year, I will fast the ninth [along with the tenth in order to differ from the Jews].” [Muslim]
Besides, Ibn ‘Abbaas narrated that the Prophet said: “Fast one day before it and one day after it.” [Ahmad]
In fact, this does not contradict the fact that the Hijri calendar was initiated during the caliphate of ‘Umar because the lunar months were known before that, but the Hijri calendar was introduced from that date when people needed it.
For more benefit on the day of ‘Aashooraa’, please refer to Fatwa 32561 and 31688.
Allaah Knows best.