All currencies are expanded when institutions begin loaning currency. How will bitcoin limit this growth? In economics there are several definitions of money such as M2, M3, etc.
The number of bitcoins in existence is limited to 21 million. This is the equivalent of M0, the monetary base. Whatever institutions do with it, creating M2, M3 etc. is not something that Bitcoin can or will control.
Here is some more info on the Bitcoin wiki: Controlled Currency Supply
If I lend a bitcoin to you, you are probably going to want me to transfer it to you. That transfer sends the one bitcoin out of my wallet and into your wallet.
There was no increase in the bitcoin money supply from that.
Let's say that I am a merchant and I sell to you a widget and extend to you payment terms in which you would pay one bitcoin due in 30 days. In this transaction, there were no bitcoins that changed hands or were required in any wallet but there was a debt created for one bitcoin. This is simply a debt though and is not an increase in the bitcoin money supply. There was no Bitcoin money created by me in this instance.
Next consider a Bitcoin bank that takes bitcoin deposits and lends out bitcoins. A Bitcoin bank can only lend out bitcoins from either its investment capital or from customer deposits. This is unlike a bank that lends out fiat that is created by a central bank. This Bitcoin bank can still do fractional reserve banking (i.e., only keep a faction of the amount of customer bitcoin deposits) but this does not increase the bitcoin money supply. There were no bitcoins created by the bank by borrowing from a central bank and then lending them out.
There is the possibility that a Bitcoin bank could issue a check payable in bitcoins to a borrower where the borrower then uses that check for payment to a supplier, for instance. But that check isn't money and the supplier can refuse to accept it as payment. Thus these checks also do not increase the bitcoin money supply.
If these checks were to begin to circulate as currency, then that is a creation of a financial instrument that is separate from bitcoin. If the bank were to issue checks for amounts that were not backed with bitcoins then that could be a form of money creation whose supply could be inflated by the debt however that money supply is not the bitcoin money supply and vice-versa.
You are right in saying that the money supply of a currency is expanded through lending. It's even possible when the currency solely consists of physical coins. This was already usual practice in ancient banking operations and is nothing new.
Since there is no Bitcoin central bank, there is no reserve requirement and the Bitcoin money supply can theoretically grow indefinitely (the money multiplier is infinite). In my opinion this means the term "fractional reserve banking" does not apply. In the case of Bitcoin we simply speak of lending. FRB only applied, if there was a central bank that sets a reserve ratio like with fiat currencies.
Despite the fact that there is no reserve requirement, Bitcoin lending will probably be limited by the deflationary nature of Bitcoin itself. I just published this article about the topic. A deflationary currency like Bitcoin provides a higher incentive to build savings instead of inducing to borrow money. Therefore lending activities in relation to the monetary base (mined Bitcoins) will remain much smaller than with fiat currencies. The Bitcoin money supply manages itself and should remain at a reasonable level.
Bitcoin is very different in that noone can control the amount of coins. The system is limited to 21 million coins. Last coin will be minted in 2140.
How the currency is minted is not something a single person can control. If you try to change the system you are no longer compatible with the other Bitcoin clients.
The system has rules so that Bitcoins are created as awards to those who contribute their computer power to secure the system and calculate/distribute transactions. This cost energy and anyone can do this.
This means that its the first truly democratic electronic currency, since there is noone who have monopoly on creating the currency.
It is also akin to looking for gold and finding it, a process you can not control. But anyone can do. The more resource you spend the more likely you are to find gold. However you are in competition with others doing this and the less energy you spend the more you earn.
There is thus a built in evolution into the system.
Bitcoins are thus not created out of nothing, but out of real energy.
Thus in order to lend out a Bitcoin you must first have it. Thats how people think the banks work.
FIAT currency is simply created with the press of a button whenever someone takes a loan. This leads to a constant loss in value, known as inflation which might be good for a country.
But bitcoin is not in a country its on the internet.
97% of the FIAT currency are created "expanded" in the private banking system given out as loans. That means that of all the currency you have in your hand, 97% of should be payed back to a bank, and even more since the banks also ask for interest rate on this money created out of air.
Bitcoins can not be payed back since they are not created out of a loan. Since they are not borrowed into existence they do not come with an interest rate.
Bitcoin is the worlds first electronic debt free currency system.
Bitcoin is the only electronic currency someone can truly own, in the sence that it should not be paid back and in the sence that it can be in 100% control of only the owner.