First of all how did you know that these parts of the world have no Muslims ? or at leas some that knows about Islam ? (you are just assuming without any facts) especially that today communication methods are easily and in everyone's hand.
Second, ALLAH will only ask people who received Islam in a way or another and didn't believe, the ones who didn't reach Islam by any mean or Islam reached them but not correct and deformed by any mean wither will be tested in judgment day or it is said that they will not be punished according to many scholars such as (Al-Ghazali).
This was taken according to these two verses:
Whoever is guided is only guided for [the benefit of] his soul. And whoever errs only errs against it. And no bearer of burdens will bear the burden of another. And never would We punish until We sent a messenger. (Surt Israa - 15)
مَّنِ اهْتَدَىٰ فَإِنَّمَا يَهْتَدِي لِنَفْسِهِ ۖ وَمَن ضَلَّ فَإِنَّمَا يَضِلُّ عَلَيْهَا ۚ وَلَا تَزِرُ وَازِرَةٌ وِزْرَ أُخْرَىٰ ۗ وَمَا كُنَّا مُعَذِّبِينَ حَتَّىٰ نَبْعَثَ رَسُولًا
(15 الاسراء )
It almost bursts with rage. Every time a company is thrown into it, its keepers ask them, "Did there not come to you a warner?"
 They will say," Yes, a warner had come to us, but we denied and said, ' Allah has not sent down anything. You are not but in great error.' "
 (surt Al-Mulk 8-9)
كُلَّمَا أُلْقِيَ فِيهَا فَوْجٌ سَأَلَهُمْ خَزَنَتُهَا أَلَمْ يَأْتِكُمْ نَذِيرٌ . قالُوا بَلَى قَدْ جَاءَنَا نَذِيرٌ فَكَذَّبْنَا (سورة الملك : 8،9).
Third don't forget that, ALLAH said:
وَلَوْ شَاء رَبُّكَ لآمَنَ مَن فِي الأَرْضِ كُلُّهُمْ جَمِيعاً أَفَأَنتَ تُكْرِهُ النَّاسَ حَتَّى يَكُونُوا مُؤْمِنِينَ
(سورة يونس - 99)
And had your Lord willed, those on earth would have believed - all of them entirely. Then, [O Muhammad], would you compel the people in order that they become believers?
So, the purpose is ALLAH's will and these are his creatures, and that is enough.