Let s,m,n be positive integers and F be a graph. A graph G is called F-saturated if F is not a subgraph of G but G+e contain a copy of F for every edge e∈E(G¯), where G¯ is the complement graph of G. Let sat(n,F) be the minimum number of edges over all F-saturated graphs with order n and Sat(n,F) denotes the family of F-saturated graphs with sat(n,F) edges and n vertices. Let mK2 denote a matching of size m and let sK2f denote a fractional matching of size s. In this paper, we determine the exact value of sat(n,mK2), and characterize Sat(n,mK2) when n+2m<n<3m. Moreover, we also determine the exact value of sat(n,sK2f), and characterize Sat(n,sK2f) when n>2s. The main results provide partial answers to the open question posed by Faudree et al. (2011).