All perfect praise be to The Lord of The Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
It is lawful for a Muslim to observe voluntary fast on any given day, except days forbidden by Sharia, such as the Day of Eid. It was narrated that the Prophet(PBUH) said, ""Whoever fasts one day in the cause of Allah, the Mighty and Sublime, Allah will separate his face from the fire by (a distance of) seventy years."{Bukhari}.
Therefore, there is no harm in observing voluntary fast on a day that coincides with a non-Islamic feast day. Al-Imam Ash-Shirbini stated, "It isn`t dislikeable for a Muslim to observe voluntary fast on a day that coincides with a non-Islamic feast day, such as the Persian New Year`s Day."{Moghni al-Mohtajj, 2/185}.
However, it is dislikeable to observe fast on that particular day intentionally."The author of the book "Fatawa At-Tatarkhania" stated:"It is dislikeable to observe fast on "The Persian New Year`s Day" while it didn`t coincide with the person`s habit of fasting on that day."{Hashyat Ibn Abdeen, 2/375}. And Allah knows best.