  We prove fractional boundary Hardy's inequality in dimension one for the
critical case $sp =1$. Optimality of the inequality is obtained for any $p$.
The extra logarithmic correction term appears in usual fashion. We also provide
a concrete (workable) example of a sequence of smooth functions that converges
to constant function in $W^{s,p}((0,1))$ for $sp=1$ and $p=2$.
