"The Türkmen Dynasties," by H. R. Roemer, from Cambridge History of Iran, Volume 6 (New York, 1986), Chapter 4, pp. 147-188, and bibliography, in 63 bookmarked and searchable pdf pages. Chapter 4 focuses on the 14th-15th centuries. Wikipedia has a main entry on the history and culture of the Turkmens (who have played a major role in world history), and a group of related entries. Internet Archive has a selection of works relating to Turco-Mongolica (various periods).
Introduction: The Turkish Background Origins and Early History of the Two Turkmen Groups Jahan Shah Qara Quyunlu The Rise of Uzun Hasan Aq Quyunlu Map. Eastern Anatolia, the Caucasus, and Azerbaijan in the Turkmen Period The Heyday of the Aq Quyunlu The Decline and End of the Aq Quyunlu Map. The Empire of Uzun Hasan Qara Quyunlu Genealogy Aq Quyunlu Genealogy Bibliography