Since i joined bitcointalk forum i find it difficult to make a post relating to bitcoin, bitcoin is like physical money (fiat), and i want to know the difference between fiat and bitcoin, and without fiat existence can bitcoin have a name?, after thinking all this with seriousness i concluded that bitcoin and fiat works like brothers and sisters and no one can leave each other, so i want to know if any other digital currency can function without fiat?.
Bitcoin is completely separate from Fiat. It works without Fiat and doesn't need Fiat to work.
So your question is answered with a big:
Yup! Bitcoin can exist without any Fiat currencies around it.
The big difference is that Fiat money is just created / issued out of thin air by printing pieces of paper and saying they have a value, while Bitcoin needs work (PoW) to be performed to be created.