I'm currently looking into the Ottomans (full disclosure, it's for an essay) and their rise to prominence prior to the fall of Constantinople, and all the sources I've found have just attributed it to a weakened Byzantium, fractured political climate and the prominence of Islam within their elites. But surely this would also apply to any number of the other Turkic states in Anatolia, so what made the Ottomans special that they were able to become the major power and last for six centuries? Or does anyone know of something that could point me in the right direction, at least (since I know AskHistorians doesn't like to do work for people?)
Simple. Ottomans were largely left alone by their neighbouring Turkic states due to the fact that they were expanding towards a Christian target. That mentality was called "Gaza", I guess you could call it a kind of a holy duty among Muslim raiders. Gaza dictates that the Ghazi(the people who take part in it) is to be assisted at all costs, locking a Ghazi state in a power struggle among the Turkic elite would have been quite the opposite.
So, raiding they did. Simply put, Ottomans gathered the Turkmen(Oghuz Turks who managed to retain their nomadic roots) under their banner using the Ghazi propaganda, pillaged Byzantine territory to the point they they could just "buy" their neighbours(which they also did, to some degree), and consolidated their power in Anatolia with their newfound riches and manpower. That's about it for the "an empire is born" part of your essay.