  The central aim of this paper is to study (regional) fractional Poincar\'e
type inequalities on unbounded domains satisfying the finite ball condition.
Both existence and non existence type results are established depending on
various conditions on domains and on the range of $s \in (0,1)$. The best
constant in both regional fractional and fractional Poincar\'e inequality is
characterized for strip like domains $(\omega \times \mathbb{R}^{n-1})$, and
the results obtained in this direction are analogous to those of the local
case. This settles one of the natural questions raised by K. Yeressian in
[\textit{Asymptotic behavior of elliptic nonlocal equations set in cylinders,
Asymptot. Anal. 89, (2014), no 1-2}].
