[opportune]

Fractional reserve banking doesn't require central banking either. It only requires that people accept more abstract forms of money such as bank notes, and that not too many people try to withdraw their money at the same time.

There's no mandate that bank notes need to be issued by a central bank. See the article: https://en.wikipedia.org/wiki/Banknote

[ThomPete]

"National banknotes are generally legal tender, meaning that medium of payment is allowed by law or recognized by a legal system to be valid for meeting a financial obligation."

So yes it requires a central bank as it's through them the recognition happens. Philosophically all money requires is trust no matter what not even a legal entity as long as people trust it, but practically to claim that central banks aren't needed for FRB is wrong to the best of my knowledge.