Can someone see a way to find an expression for $g(t)$ defined as inverse Laplace Transform below? Perhaps in the limit of large $t$
$$g(t)=\mathcal{L}^{-1}\left[\frac{I(s)}{\frac{1}{J(s)}-1}\right](t)\\ I(s)=\int_0^\infty \mathrm{d}i\ \frac{h(i)}{s+2h(i)}\\ J(s)=\int_0^\infty \mathrm{d}i\ \frac{h(i)^2}{s+2h(i)}\\ h(i) = \frac{(1+i)^{-p}}{\int_0^\infty \mathrm{d}j\ (1+j)^{-p}}\ \\ p>1$$
Motivation: this gives a way to approximate $g(t)$ in the in this question for $a=-2,b=1,h(i)=\ldots$
I can solve it numerically for $p=1.1$, but interested in symbolic form
