Let $f(t)$ be a function (for example of time $t$).
Is there a general expression of the laplace transform of $\sqrt{f(t)}$ ?
Same question for the inverse Laplace transform : Let $f(s)$ be the Laplace transform of $f(t)$, is there a generic expression of the inverse Laplace transform of $\sqrt{f(s)}$ ?
edit: One special case is known: the Laplace transform of $f(t)=t$. It is often tabulated, like in this table from Lamar University, Texas.
edit2: I have no idea how to prove such a general transform exists. Perhaps it does not and in this case I would be very grateful for a link or an explaination.