There's an out of print book (1978) that's a good starting place. Its titled Philosophy East/Philosophy West: A Critical Comparison of Indian, Chinese, Islamic, and European Philosophy there are 5 authors, the fist two listed are Ben-Ami Scharfstein and Ilai Alon. The authors, after tracing Greek philosophy through the Islamic world, states (p 50):
...Islam belongs philosophically to the Western tradition. I admit that is reducing the number of 'philosophical civilizations' to three [Indian, Chinese, Western] I have been motivated in part by the desire to keep a complicated comparison from growing more so; but I should not have made the decision without what appears to most scholars good reason.
Let me explain myself. The Islamic world is clearly just as worthy of demarcation as the Greco-Roman, Indian, Chinese, or later European worlds. Like the others, the Islamic world was a synthesis drawing on my sources, in its case, Greek, Jewish, Christian, and Iranian, all these unified by its religion, its tradtions, and its revered language, Arabic. It ought to be added, to emphasize the physical dimensions of the synthesis, that the Islamic empire at it height was far greater than the Roman. In relation to philosophical thought, however, the Muslims were basically dependent on the Greeks. Unlike the Greeks, or, for that matter, the Indian or Chinese, they did not have to create philosophy ex nihilo, for history had already provided them with a beginning, Greek, or, rather, Hellenistic philosophy, which they exploited, varied, and sometimes extended with great energy and talent.
and on page 51:
...Islamic thought was inevitably influenced by Indian thought, and there have been scholars who have judged the influence to be strong. THe bold though distinctly atypical al-Razi has been supposed to owe a good deal to Indian influence; the atomism of Islamic theology, kalam, has been supposed to have been largely borrowed from India; and there was certainly some interaction between Islamic and Indian mysticism. But even a partisan of Indian influence is likely to agree that it did not change Islamic philosophy in any basic way.
The relationship between Islamic and Greek philosophy is far more evident and powerful. The Arabic word for 'philosophy' falasafah, meaning, essentially, Aristotelianism (with Neo-Platonic interpolations), indicates where Islamic philosophy originated; and even kalam, which polemicized against the Aristotelian philosophy, would have been impossible if not for Greek ideas and philosophical techniques.[follows a quote from ninth century philosopher Al-Kindi justifying his dependence on Greek philosophy and an eleventh centuty Arab scholar in the same vein]
they then conclude this section (p 52) with:
...the civilizations of Greece, Roman, the Christian West, and Islam (including Judeo-Islamic thought) are branches of the very same tree.
In sections where they do comparisons of Indian and Chinese to the West, they include many examples from the Islamic tradition as part of the West.