Why were the Ottomans so successful in the 14th and 15th centuries?

At the beginning of the 13th century, the Ottomans were one of the numerous nomad Turkish tribes present in Anatolia since the battle of Mantzikert at the end of the eleventh century. They probably formed one of the Oghuz tribes, the tribal family which gave birth to the Seljuk dynasty. Besides, these tribes were vassal to the Seljuk empire and they received an itqa in exchange for military service.1 More precisely, these tribes were under the control of the Rum sultanate, a minor part of Seljuk dynasty, which ruled Anatolia and which continued to prosper in spite of the collapse of the Seljuk empire in the rest of the Islamic world. However, around the middle of the thirteenth century the Mongol invasions directed by Genghis Khan destroyed the Sultanate of Rum. Thus it was the beginning of a period of ''anarchy'' in Anatolia and most of the Turkish tribes became independent.
Osman was the chief of one of these small emirate created after the collapse of the Seljuk of Rum and give his name to the dynasty ( The Ottomans were the partisans of Osman).
Three centuries later the Ottomans ruled a very large territory. As they controlled the Holly cites of Mecca and Jerusalem and some very important Islamic cities as Baghdad, Damascus they could be considered as the leaders of Islamdom. Moreover as they ruled Constantinople since 1453, they could be considered as the symbolic heirs of the Roman Empire as well.2
Thus the 14th and the 15th centuries were determinative for the Ottomans, indeed it is during this time they build up their empire. Then, it is interesting to examine the reason of this success.

I. A clever politic of extension.

The Ottomans were maybe distinct to the other Turkish tribes in raison of their geographic settlement in Anatolia. Originally the little Ottomans state were situated to the north west of Anatolia, a frontier zone with the Byzantine empire. As the Ottomans