This is a simple python logic you could find by googling.

You can use relativedelta library for that.

from dateutil.relativedelta import relativedelta

# Convert string date value to datetime object
current_date = fields.Datetime.from_string(self.current_date)

# Increment the added_date by given months 
added_date = current_date + relativedelta(months=self.exp_month)

self.write({'added_date': added_date})