Recently I have learned that "I.S" (Islamic State) has hanged till death two girls for not Fasting.

I want to know that which line of the Holy Qur'an is supporting this rules ? Does Islam support this ? How would you judge this ?

The Qu'an does NOT support such barbarism.

The Punishment for not fasting during Ramadan (without a valid excuse) | The Greatest Month (http://thegreatestmonth.com/2010/08/08/the-punishment-for-not-fasting-during-ramadan-without-a-valid-excuse/)

My interpretation based upon what is read, and please read through what fr_chuck posted, is that the punishment for breaking your fast without a valid excuse is hanging doesn't have a base in the Quran based upon the common reading of it.

The problem that comes when you try to apply something from a holy book into real life is that it is often based upon an interpretation of the reader. For instance, and it was in the above link, it was said that if you break the fast then you've not accepted Islam and are not able to be targeted as one would target a non-islamic individual. Considering the Islamic State's general approach to non-muslim individuals is generally not favourable and somewhat violent at times, this result is not surprising.

The second problem is those who will only interpret the passages that support their cause and beliefs while ignoring those that refute their stance. As stated in the above link, and through general agreement of most of Islam, when someone falls away from Islam they've committed a grave sin. Allah is a kind and forgiving God and accepts all those who repent their sins, regardless of the severity of them, thus if someone has broken their fast, fallen away from Islam, and wants to new their commitement to Islam then all they have to do is repent for their sin and accept Islam again. This includes resuming their fasts.

This kind of radicalization of a faith has been seen in many different faiths. The leaders use the faith, their charisma, and manipulation to gain power over their followers and allow them to do what they leader wants without putting the leader in danger. Religious cults in the US. The IRA in Ireland, IS in Iraq and Syria, Taliban in Afghanistan, North Korea, and many, many more currently. It gives a improper image of what each faith is and how it affects its followers.

I want to make it quick & simple, ISIS are against God , here is the reason :
God said in quran : "killing one innocent person is equal to kill all humanity in the earth" , they kill innocent people and they aren't follower of Islam and they are not MUSLIMS , because their deed is not based on Quran (every line of quran is word of the GOD (allah) , they just kill people for no reason , that's all

And for fasting , it's a muslim duty to do this and the god only can judge people , we are not god to judge people and punish them