The best comprehensive book I know is Cristoph Baumer, The History of Central Asia. The first half of the period you are after is covered in volume 3 ("The Age of Islam and the Mongols"), which covers from the Abbasids through to Timur. The second half of your period will be covered in volume 4 ("The Age of Decline and Revival"), which is due for publication in August 2018 (and will be the final volume in the series).

There is a lot of interesting material in UNESCO's History of civilizations of Central Asia. Your period is covered in vol 4 part 1, vol 4 part 2, and vol 5. These books are available online as pdfs on UNESCO's website:

• V4 part 1: http://unesdoc.unesco.org/images/0011/001116/111664eo.pdf

• V4 part 2: http://unesdoc.unesco.org/images/0012/001204/120455e.pdf

• V5: http://unesdoc.unesco.org/images/0013/001302/130205e.pdf

For a single-volume coverage of your period, there is volume 2 of The Cambridge History of Inner Asia, "The Chinggisid Age". Not as comprehensive and detailed as the other books above, but still quite good. The book covers Central Asia from c. 1200 to 1700 in plenty of detail (parts 1-4), and continues through to the 19th century (in part 5). The publisher's website for the book, where you check the contents in detail (as in, download the contents pages to see what is covered in the various parts and chapters), is http://www.cambridge.org/gb/academic/subjects/history/regional-and-world-history-general-interest/cambridge-history-inner-asia-chinggisid-age

Finally, Svat Soucek, A History of Inner Asia, Cambridge University Press (2000) is a good comprehensive introduction. Less detailed, and covers a wider period than you are interested in under 400 pages, so doesn't have close to as much detail on 1200-1700 as the above books.