With the exception of Bank Asya, I believe most of the other major "Islamic" lenders in Turkey are part owned by Middle Eastern countries.
Truth be told, the practice of Sukuk (Islamic lending) is just a pretty convoluted way round charging interest. In simple terms - Wullie wants to buy a house, so a middleman buys it (Wullie moves in) and sells shares in it to "investors" who then receive "rental" at an appropriate level in relation to the value of the house from Wullie. Once enough "rental" has been paid, Wullie buys the house from the shareholders at an agreed (usually nominal amount) price.
Turkey is getting heavily into Sukuk - one law firm in Istanbul is doing a lot of business involving this sector. Big bucks involved.
JF