The text I see cited most often is Murray Gordon, Slavery in the Arab World (New York: New Amsterdam Books, 1989). It's a quick and easy once-over, but it's got some major historical problems. Gordon often throws sources from different places and different centuries together as if they describe the same system of slavery, when there must have actually been a broad diversity of changing slave institutions over the period that he studies. So it's a good introduction, if read with caution.

Since this isn't quite my area of research, I can't point you to other recommendations that I've read. However, a quick cull of bibliographies turned up:

• James Watson, ed., Asian and African Systems of Slavery (Oxford: Basil Blackwell, 1980).

• David Eltis and Stanley L. Engerman, eds., The Cambridge World History of Slavery Volume 3: AD 1420–AD 1804 (Cambridge: Cambridge University Press, 2011).

You might also want to do a quick google of the individual essay writers in each of these volumes, to see if they've got anything else that sparks your interest.

Finally, for a bit of comparative history, albeit not exactly with the focus you're looking for, I'd strongly recommend John Thornton, Africa and Africans in the Making of the Atlantic World, 1400–1800, 2nd edn. (Cambridge: Cambridge University Press, 1998). It's a great read!

Others are pointing you to sources, but to answer the question in your title, one thing that becomes apparent very quickly when you study non-Western history is that Western history has vastly more research and publication on it than non-Western history. To give an example, there has been far more academic research and publication on Late Antiquity (between about 300-600) alone than on the entirety of dynastic Chinese history (this comes from Walter Scheidel's Rome and China). And even outside of western history proper, generally speaking the areas with the most research are when westerners are involved: I would wager that there is more published on the fifty years between the Opium Wars and the fall of the Qing than on the Song Dynasty.

A lot of this is simple ease of research. This has come up very frequently in Indian Ocean studies, but studying, say, the Persian contribution to the trade requires a much more specialized language study than, say, the French one, simply because historians tend to pick up French in graduate school no matter what, and graduate programs often require learning French, German and maybe Italian. This sort of requirement base penalizes anyone who wants to study the Persians, as they will need to wade through an entire additional skill set in order to reach their area of study. And so people are incentivized to continue being parochial regarding Westerners and the narrative develops (still common in many general works!) that westerners were the drivers of the dynamic early modern Indian Ocean, despite there being far more Persians involved!

Luckily this is is re-balancing, but until the study of history as a whole stops being so incredibly Western (ie, locations of universities) this will likely continue, and be the answer to "why is the non-western x so understudied?"

Hi there, there is always more to be said on the topic, but you may be interested in these recent answers from /u/sunagainstgold and /u/sowser:

"In Diarmaid MacCulloch's "the Reformation," he claims over a million western Christians were enslaved by Islamic corsairs in the 16th and 17th centuries. What happened to these people?"

"Why is their a relatively small African diaspora population in the Middle East despite the fact that the Arab slave trade brought millions of Black slaves from Africa to the Arab world for more than a thousand years?"

Could you expand a little more about what you mean by non-Western slave trade? Are you talking about Barbary coast slavers, or "Irish slavery" or indentured servitude, or something else? Or maybe all of the above?

I hesitated to post because my sources seemed a bit old, but I see I'm in good company.

The topic's now sadly so politically and culturally charged that I doubt any contributor will escape controversy for a while. I suspect the challenge of quantification may have deterred many: even the best estimates of single authors can range by a factor of five, while totals of broadly the same order of magnitude as the Atlantic trade make any count doubly likely to be pounced on for suggesting either to be the greater evil.

I think Clarence-Smith (ed), The economics of the Indian Ocean slave trade in the nineteenth century (1989) remains a good introduction for the late period though it's now a bit old. The African slave trade from the fifteenth to the nineteenth century (Unesco General history Studies & monographs 2, 1979) is mostly about the Atlantic trade but has useful summaries of findings of the time. I'm really a bit stumped for comparable recent surveys, so I'll be wading through the answers looking for suggestions too.