Tetrations of non-integers? [duplicate]

A Tetration is defined as $${^{n}a} = \underbrace{a^{a^{\cdot^{\cdot^{a}}}}}_n$$ or, by a recursion function, $${^{n}a} := \begin{cases} 1 &\text{if }n=0 \\ a^{\left[^{(n-1)}a\right]} &\text{if }n>0 \end{cases}$$ That is, iterated exponentiation (like exponentiation is iterated multiplication). Exponentiation can be expressed as $e^{n\ln a}$ [1]

Is there a like way to express Tetrations? That is, a way to calculate for both negative and decimal Tetrations?