  For any two distinct vertices $x$ and $y$ of a graph $G$, let $S\{x, y\}$
denote the set of vertices $z$ such that either $x$ lies on a $y-z$ geodesic or
$y$ lies on an $x-z$ geodesic. Let $g: V(G) \rightarrow [0,1]$ be a real valued
function and, for any $U \subseteq V(G)$, let $g(U)=\sum_{v \in U}g(v)$. The
function $g$ is a strong resolving function of $G$ if $g(S\{x, y\}) \ge 1$ for
every pair of distinct vertices $x, y$ of $G$. The fractional strong metric
dimension, $sdim_f(G)$, of a graph $G$ is $\min\{g(V(G)): g \mbox{ is a strong
resolving function of }G\}$. In this paper, after obtaining some new results
for all connected graphs, we focus on the study of the fractional strong metric
dimension of the corona product, the lexicographic product, and the Cartesian
product of graphs.
