Let L = {a1/b1,..., as/bs }, where for every i ε [s], ai/bi ε [0, 1) is an irreducible fraction. Let F = {A1,..., Am} be a family of subsets of [n]. We say F is a fractional Lintersecting family if for every distinct i, j ε [m], there exists an a b ε L such that |Ai ∩ Aj| ε {a/b |Ai|, a/b |Aj|}. In this paper, we introduce and study the notion of fractional L-intersecting families. © The authors.