Fractional reserve banking doesn't require a central bank to exist or work, but it does need something physical that backs whatever the bank is holding/issuing.  But since 1913 it has implied a central bank exists.

You could create a bank where deposits are denominated in BitCoins and depositors receive some interest for keeping their coins in the bank instead of a private wallet.  There are so many issues with this that it seems inconceivable. 

FRB can work if the bank actually holds considerable reserves for it's liabilities.  This implies fewer pieces of money or dollars or whatever you want to call it being used in the economy.