After installing "Dragonborn" DLC, two people came and informed me about the Dragonborn in Whiterun, and then attempted to kill me. So after whooping their buttocks I continued with the game and around two weeks of in game time has bassed, but everytime I visit "Whiterun" their corpse are just lying there.

I'm assuming this is a glitch considering the bodies normally disappear after your next visit.

How can I fix this problem?

Hello?!?!

Not all bodies vanish, these ones never will. Make ash piles out of them or dump them some where where they cannot be seen, like under the bridge near the smiths.