I wonder if the knowledge basis of the LaPlaceTransform anf the InverseLaplaceTransform is complete. In Particular, I Have tried to find the InverseLaplaceTransform of $s^{-\alpha}$ without any result if $0< \alpha <1$. I need to use Caputo fractional derivative, so if I am true, how can I complement the knowledge basis of LaplaceTransform and InverseLaplaceTransform. Has a specific package developped for this subject ?
Thanks
You can add definitions to InverseLaplaceTransform by something like:
Unprotect[InverseLaplaceTransform] InverseLaplaceTransform[s_^-a_, a_, t_] := outcome
But be careful what you redefine, if you do it wrong it can lead to disastrous results...
