The code seems to be correct, but it takes too long to calculate.
If I call
InverseLaplaceTransform[1/(s + ak[s]), s, 0.2]
it works forever, but I don't get the input back. From a cursory look, it seems that you are nesting three levels of NIntegrate. It is not surprising that it takes forever.
NIntegrate
Kindly, can you provide the correct code for the above calculations. Many thanks in advance
