Shariah law forbids charging interest, speculation, options, futures, derivatives, etc. Much like concurrent canon law and our modern-day democracies, the financial regulations were really just political promises to rally the peasants to their side against private power.
It seems to me that the only reason it forbids fractional reserves is because all transactions must have "material finality". This boils down to picking your poison. Do you want fraudulent banking, or do you want dysfunctional banking?