This evening marked the start of the new Islamic year, 1435 to be exact.
The same vocabulary applies here as it did to the Gregorian New Year. “New Year” will be Yeni Yıl, the literal translation, or Yılbaşı, the “start of the year.”
“Happy New Year” is Yeni Yılınız kutlu olsun! or “May your New Year be blessed!”
Turkish Word a Day 