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From: dimanag78@gmail.com
Newsgroups: comp.soft-sys.math.mathematica
Subject: inverse laplace transforms
Date: Tue, 4 Mar 2014 06:52:25 +0000 (UTC)
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Hello to all.

It has been years since I last made a post:-)!

A colleague of mine gave me the following

InverseLaplaceTransform[1/(1 + (a*I*s)^(-b)), s, t]

Mathematica 8 returns the transform unevaluated.

The values of the parameters are:
0<b<1
0<a<10

I am puzzled with the behavior of the integrand.
For a=2 and b=3/10 e.g. there is a branch cut along the imaginary axis.
I cannot figure out the positions of poles.

Any ideas of evaluating symbolically (or numerically) this inverse transform?

Thank you very much in advance for your response.

Dimitris Anagnostou
Postdoc Researcher, Arts et Metiers, ParisTech, Metz