You should not fast on these days.
Especially if jews did so.
After the hijrah when the Prophet (peace and blessings be upon him) came to Madinah, he found that the Jews of Madinah also used to observe this day with fasting. The Prophet (peace and blessings be upon him) asked them the reason of their fasting on this day. They said, “This is a blessed day. On this day Allah saved the Children of Israel from their enemy (in Egypt) and so Prophet Musa fasted on this day giving thanks to Allah.” The Prophet (peace and blessings be upon him) said, “We have more claim to Musa than you.” He fasted on that day and commanded Muslims to fast on this day. (Al-Bukhari, hadith 1865)