Find Inverse Laplace Transformation of the given function?

Questions
1

Consider the following code:

InverseLaplaceTransform[1/(s - s^(\[Alpha] + 1) - \[Lambda]), s, 
      t] // FullSimplify
2

Using:

\sum _{j=0}^{\infty } -s^{(1+j) (-1-\alpha )} (s-\lambda )^j=-\frac{1}{-s+s^{1+\alpha }+\lambda }

then we have:

 Sum[FullSimplify[
   InverseLaplaceTransform[-s^((1 + 
         j) (-1 - \[Alpha])) (s - \[Lambda])^j, s, t], 
   Assumptions -> {t > 0, \[Lambda] > 0, \[Alpha] > 0}], {j, 0, 
   Infinity}]
\sum _{j=0}^{\infty } -t^{(1+j) \alpha } \, _1\tilde{F}_1(-j;1+\alpha +j \alpha ;t \lambda )

I doubt there’s a closed form for the series.

Regards M.I.

3

Thank you very much Sir.
Closed form is not issue.