Which one is correct to describe a photographer who lives in an arabic country ?
(arabic photographer) Or (arab photographer ) Or (Arabian photographer)
And what are the differences
Arabic photographer - I'd understand this in context, but it's a little odd. Arabic normally refers to the language.
Arab photographer - This is fine. It most likely means a culturally and ethnically Arab person who takes photographs. The person could live in (for example) Saudi, Libya or Germany but still be an Arab photographer. It could also mean a person who photographs Arabs, but this seems unlikely. An Arab is a person, here it is being used as an attributive noun.
Arabian photographer - This is also fine. It has the possibility of meaning "a person who takes photos of Arabian scenes. Arabian is an adjective that can describe both people and things. Arabian refers particularly to the Arabian peninsula, and not to North Africa.
Consider using a particular county's name: a Saudi photographer, or an Egyptian photographer, for example.
There's a discussion of these three adjectives on Professor Paul Brians of Washington State University's website.
In it, he states:
Arabs are a people whose place of ethnic origin is the Arabian Peninsula. The language which they speak, and which has spread widely to other areas, is Arabic. “Arabic” is not generally used as an adjective except when referring to the language or in a few traditional phrases such as “gum arabic” and “arabic numerals.”