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

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?

• Where did the expression come from? Did you perform a Laplace transform first, simplify and now need to do the inverse Laplace transform? – John Habert Feb 7 '14 at 18:29
• @JohnHabert: I am solving coupled partial differential equations(space and time) with a complicated boundary conditions. So, I solved it in Laplace domain and now I am trying to invert the solution. – tumchaaditya Feb 8 '14 at 19:46

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