There is at least one Arabic fighting manual which I know for a fact exists, it has a very long name but I'm fairly certain the first part of the title is "kitaab al furesiya". It focuses on the use of a curved "saif" (which just means sword in Arabic, whether straight or curved) On foot and on horseback, and I believe there is also a mounted archery section, but I'm not totally sure. Many others probably exist but they are more or less in an undiscovered state similar to much of our MARE material had been until recent decades. There are also Persian fighting manuals, and Turkish ones as Stacy mentioned. I do believe however that the clay cutting image Stacy described may actually be in the Arabic fighting manual Kitaab Al Furesiya because I remember seeing an image of cutting at clay in that manual when I stumbled across an online copy which I have since lost the link to

. (Or perhaps clay was a common test cutting medium in the Middle East?)
There is a long standing Persian grappling tradition inside Persian traditional gyms known as Zoor Khane or "House of Strength" Which definitely qualifies as a martial art, but which may have been ritualized to the point of non-martiality in the modern world, although again I'm not really certain as I have not had the opportunity to grapple in a Zoor Khane and determine how martial the focus is today, and it also probably varies from gym to gym.
Arabic, thankfully, has actually changed very little from the days of the 7th century to the present, and a person who has a high fluency in Modern Standard Arabic could probably understand one of these manuals without too much difficulty once they got through and overcame the obviously technical language related to swords and their use which would be found in such material.
Interestingly, swords in the Middle East, particularly in the Arab world, were typically actually straight double edged weapons with either cruciform, or downward curving cruciform hilts, during the period of the Crusades, and it was actually Turkish influences from Central Asia in the 14th-15th centuries who brought the popularization of the well known "scimitar" shape into the region.
I think it would definitely be interesting if any of these manuals and Middle Eastern fighting arts were to be uncovered in greater depth by somebody to make a comparison between our Art, and those of the Middle East. Our Arts are compared to death with those of Asia, a part of the world they had fairly limited contact with. But throughout the period we study there was frequent warfare between Europe and the Middle East and the two would in fact be a far more appropriate comparison.