First of all please let me take a stance regarding fractional reserve banking: accepting deposits, putting a fraction aside and lending out the remainder is the standard way any and all banks operate, regardless if they use gold, green paper or bitcoins. The notion that fractional reserve banking is somewhat only possible if enabled by a central bank is a Zeitgeist conspirationista type of fallacy. One who doesn't understand what fractional reserve banking is, and the way it enables monetary expansion from M1 to M2, like our friend here AV, is nothing but a crackpot armchair economist who does not even warrant a response.
That's not what fractional reserve is. Not even close. Today, a bank makes a loan first, and then seeks new deposits to cover between 0% and 10% of it.
And yes, the central bank is exactly what makes this scheme possible. Fractional reserve lending wasn't created in 1913 when the Fed came online, but it did explode around that time. The whole point of the Federal Reserve System was to set up a bank that could create money at will and lend it to other banks when necessary. Bank runs simply do not happen now because the Fed can step in with an instant loan and prop up any failing bank. FDIC stepped it up another notch, but that is a different topic.