Inverse Laplace transform of $\large \frac{1}{s^2-As^{1.5}}$

Question

Title says it all. How do I go about finding inverse Laplace transform of that expression? If it were complete exponents, I would have used partial fractions. But what to do with non integer exponents?

Answer 1

$$\frac{1}{s^2-As^{1.5}} = -\frac{1}{A^3(\sqrt{s}+A)} + \frac{1}{A^3\sqrt{s}}-\frac{1}{A^2s}+\frac{1}{As^{1.5}}$$

The inverse Laplace transform of the first term doesn't have a closed form solution:

http://www.wolframalpha.com/input/?i=inverse+Laplace+transform+1%2F%28sqrt%28s%29%2BA%29

The rest of the terms are easy.