By 642 AD , under Caliph Umar , Arab Muslim forces had laid Placing control Control of Mesopotamia ( 638 ) , Syria ( 641 ) , Egypt ( 642 ) , and had invaded Attack Armenia , all previously territories split Motion between the warring Hostile_encounter Byzantine and Persian Empires , and were concluding Process_end their conquest Conquering of the Persian Empire with their defeat Conquering of the Persian army at the Battle Hostile_encounter of Nahāvand .