  In this paper we study ground-states of the fractional Gierer-Meinhardt
system on the line, namely the solutions of the problem \begin{equation*}
\left\{\begin{array}{ll} (-\Delta)^su+u-\frac{u^2}{v}=0,\quad
&\mathrm{in}~\mathbb{R},\\ (-\Delta)^sv+\varepsilon^{2s}v-u^2=0,\quad
&\mathrm{in}~\mathbb{R},\\ u,v>0,\quad
u,v\rightarrow0~&\mathrm{as}~|x|\rightarrow+\infty. \end{array}\right.
\end{equation*} We prove that given any positive integer $k,$ there exists a
solution to this problem for $s\in[\frac12,1)$ exhibiting exactly $k$ bumps in
its $u-$component, separated from each other at a distance
$O(\varepsilon^{\frac{1-2s}{4s}})$ for $s\in(\frac12,1)$ and
$O(|\log\varepsilon|^{\frac12})$ for $s=\frac12$ respectively, whenever
$\varepsilon$ is sufficiently small. These bumps resemble the shape of the
unique solution of \begin{equation*} (-\Delta)^sU+U-U^2=0,\quad
0<U(y)\rightarrow0~\mathrm{as}~|y|\rightarrow\infty. \end{equation*}
