Yes you can, Technically speaking.
You can chew gum when fasting BUT only if the gum is sugar and artificial sweetener free.
If the chewing gum is not sugar-free it can add to calroie intake and break a fast.
For example you may think that gum is a tiny contributor to your energy intake, BUT IF you crave more and chew more chewing gums, the calories will soonn dd up and could breach the 50 calorie threshold that will take your out your fasting state