Hi,
using caps to have two fans of 1A total running for 10 minutes would require a cap value of 600F. There are supercaps out there with a capacitance of 1,200F, but their charging voltage is limited to 2.5V.
That means you can get to approx. 12V by connecting 5 caps in series (12.5V), thereby reducing the total capacitance to 240F (1,200/5), resulting in a fan operating time of four minutes.
I suggest to use an external power supply and have the funs operating for any desired time period.
Boncuk