Storing non-Gregorian dates in Mysql’s date type

I have a mysql table that has a column with date type.
I’m going to store non-Gregorian date in this column (i.e. Jalali date).
I tested this by using phpMyadmin and storing a Jalali date and no error happend.
Is it a good idea to store non-Gregorian dates in date type?
If not; which is better? storing it as varchar or as timestamp or timestamp as Int or something else?