Laplace transform - frequency differentiation property (generalization)

Question

Let $\mathcal{L(f(t);s)}$ be the Laplace transform of a function $f$. It is known that the Laplace transform of $\mathcal{L}{(t^nf(t);s)}$ is given as (frequency differentiation property) \begin{equation} \mathcal{L}{(t^nf(t);s)} = (-1)^n \frac{d^n}{ds^n}\mathcal{L}(f(t);s), \end{equation} that is, in terms of the $n$-th derivative of $\mathcal{L(f(t);s)}$. Is there a closed-form for the folowing Laplace transform \begin{equation} \mathcal{L}{(t^pf(t);s)}, \end{equation} where $p \in \mathbb{R}$ with $p \geq 1$?