DOCTOR THOMAS SOWELL, in his very illuminating book "BLACK REDNECKS & WHITE LIBERALS" wrote a chapter, "The Real History of Slavery", in which he described the significant efforts of the British, the Royal Navy, etc., to interdict, disrupt, stop slavery, & to free slaves, in their colonized lands around the world.
It’s been a few years since I read this book, so I can’t provide quotes or anything more at this time except to say that it mentioned a number of lands on the African continent, and this would include some Muslim areas. So I commend it for your research.
This was rarely recognized fact was done, of course, after their well-known long record to profit by the Slave Trade. I also suggest you might look into England’s SLAVERY ABOLITION ACT of 1833, and the years following. That act abolished slavery throughout the British Empire; and strenuous efforts were made to enforce it in its colonies.