Equating Turks (not sure if you mean that or Ottomans?) conquering armies with "Islam conquering parts of Europe" (Greece?, Spain?) seems likely to be problematic; the latter would suggest willful adoption en masse of Islamic religion, political structure, warring.

Did the conquerors instigate Sharia, did they do the Mohammedean standard "pay jizya, convert, or die" offer to the populous? Did the conquered people convert and then seek to forcibly "convert" others?