I'm working on some differential equations for a model i'm making. I have a solution in laplace space, and I have up to this point used numerical methods to find the inverse transform. However, ideally i would like a completely analytical solution.

I've been looking in tables, but have found nothing so far. I would be extremely greatful if anyone could help find the inverse laplace transform of the function below:

F(s) = 1 / ( s + a \sqrt{s} + b) + 1 / \sqrt{s}( s + c \sqrt{s} + d)
where a,b,c,d are constants.