we have a hadith on this : When the Prophet came to al-Madinah he found that the Jews observed the fast of Ashura. He enquired about this and was told that it was the day on which God had delivered the Children of Israel from the enemy and Moses used to keep a fast on it as an expression of gratitude to the Almighty. The Prophet thereupon remarked that "Moses has a greater claim upon me than upon you," and he fasted on that day and instructed his followers to do the same.
But how are now the dates different from the Islamic Ashura?