When was fractional reserve banking introduced?
Fractional reserves banking is at least as old as the 1400's:


  A balance sheet from the London branch of the Medici Bank, dated
  November 12, 1477, shows that a significant number of the bank’s debts
  corresponded to demand deposits. Raymond de Roover himself estimates
  that at one point, the bank’s primary reserves were down to 50 percent
  of total demand liabilities. 60 If we apply the standard criterion
  used by A.P. Usher, this implies a credit expansion ratio of twice the
  demand deposits received by the bank. There is evidence, however, that
  this ratio gradually worsened over the bank’s life-span, especially
  after 1464, a year that marked the beginning of growing difficulties
  for the bank. The roots of the general economic and bank crisis that
  ruined the Medici Bank resemble those Carlo M. Cipolla identifies in
  his study of fourteenth-century Florence. As a matter of fact, credit
  expansion resulting from bankers’ misappropriation of demand deposits
  gave rise to an artificial boom fed by the increase in the money
  supply and its seemingly “beneficial” short-term effects.
  Nevertheless, since this process sprang from an increase in the money
  supply, namely credit unbacked by growth in real savings...


Page 73-74 of Money, Bank Credit, and Economic Cycles Jesus Huerta de Soto 

The Wikipedia page on Scali Bank claims that the Austrian school or at least Soto believes that fractional reserve banking did in Scali bank in the 1300's but I couldn't find evidence for the claim in the citation.

Middle eastern banks were offering transaction accounts and loans in the  7th–12th centuries and this makes it likely that fractional reserve banking was occurring there as well.