Summary: Let \(G = (V,E)\) be a connected graph and let \(k\) be a positive integer with \(k\leq rad(G)\). A subset \(D\subseteq V\) is called a distance \(k\)-dominating set of \(G\) if for every \(v\in V-D\), there exists a vertex \(u\in D\) such that \(d(u,v)\leq k\). In this paper we study the fractional version of distance \(k\)-domination and related parameters.