"circular" operators, "circular" derivatives, and "circular" tetration.

[JmsNxn]

Maybe I know little about fractional derivatives.

It says your Math Skill Level is Professor, so you should know about fractional derivatives.

So we got

D^s exp(z) = z for all complex s and z.

So what ?

Regards 

Tommy1729

That's unique. That means the fractional derivative is unique....

Like, I'm so confused by your counter arguments. They don't make any sense.

If you can prove there is a solution to your equation (your recursive equation), and you can prove it is exponentially bounded, then you can interpolate it using this fractional derivative. Additionally you can prove it is the only solution that can be interpolated in such a manner; and is exponentially bounded as such. End of story. I think you're getting hung up on using different fractional derivatives too much. I don't care about them. They do not have a uniqueness to them, they don't enter the picture at all...