Actually NO.
Arabia is a barren Desert, while Greek is mountainous. They were never very productive areas to begin with. Even persia is a barren plateau ,with large part under two deserts (dast-e-lut and Dast-e-Kavir) and Mountains. in comparision to Indo-Gangetic fertile Plains.
There are very few examples in History (probably Romans) where a prosperous sedentary civilization waged war over it's less prosperous neighbours. Even China ,inspite of all the fabrications by bot army, was never larger than UP except for short amount of time. They had no claim over Tibet and they walked into XinXiang when Soviets withdrew from that area to reinforce German border in WWII. (XinXiang was part of Soviets, not Qing dynasty.