At Alexander the Great’s death the people around him asked “To whom will you give the Empire?” His answer “To the strongest” It was, after much fighting and intrigue divided into four parts, or five if the original Greece was included.
The intertestamental period (the gap of time between the period covered by the Hebrew Bible and the period covered by the Christian New Testament) is recorded in the Apocrypha, especially the Maccabean books.
That was then, this is now. Notice the Muslim world covers much the same area as the Achaemenid Empire and of Alexander the Great, but with expansions in Africa and South Asia. It does exclude Israel, a sore point for anybody wanting to conquer the world through Jihad.