Chewing gum in which there is sugar when fasting

It seems that the questioner is referring to
the kind of chewing gum which is well known nowadays, which is a rubbery
substance that usually contains sugar and artificial flavourings. Chewing
this kind of gum leads to breaking the fast, because the sugars and
flavourings dissolve in the saliva and enter the stomach. Undoubtedly this
breaks one’s fast, because nutrients enter the stomach. But if the gum does
not contain any substance that will dissolve and enter the stomach, then it
does not break the fast. 

With regard to alternatives to chewing gum,
if what is meant is something that may be used to improve the smell of the
mouth, then the Muslim should use siwaak, because it is one of the Sunnahs
narrated from the Prophet (peace and blessings of Allaah be upon him).
He may also rinse his mouth so as to remove the smell, or use toothpaste,
subject to the condition that nothing of it reaches his stomach. If he fears
that some of it may reach his stomach then he should not use it. 

You should also note that this smell that
comes out of the mouth because the stomach is empty and which may disturb a
person, cannot be removed with the siwaak etc because it comes from the
stomach due to fasting. It is better before Allaah than the fragrance of
musk. It was narrated from Abu Hurayrah that the Prophet (peace and
blessings of Allaah be upon him) said: “The smell of the fasting person’s
mouth is better before Allaah than the fragrance of musk.” Narrated by
al-Bukhaari, 5583; Muslim, 1151. See also question no.
22913. 

But if the purpose of using gum is to treat
the jaw by means of moving it, please see question no.
38552. 

And Allaah knows
best.