What is the meaning (if any) of $D^{i}f(x)$? [duplicate]

Recently I came across fractional derivatives of functions of the type

$D^{\frac{1}{2}}f(x)$

and I was wondering if it made sense to take the $i$ derivative of a function, where $i = \sqrt{-1}$

$D^{i}f(x)$

If it does make sense, what does it mean? And how do you compute it? Thanks!

Solution 1:

Derivative of order $k$, where $k$ is a nonnegative integer, is a standard notion in calculus. Derivative of fractional order ... or of complex order ... that is not a standard notion in calculus. If you use it you should define it somehow.

One way it can be defined uses the Laplace transform. Perhaps you will study that in the future.

See HERE