Jacobson, Levin, and Scheinerman introduced the fractional Ramsey function r_f(a_1, a_2,..., a_k) as an extension of the classical definition for Ramsey numbers. They determined an exact formula for the fractional Ramsey function for the case k=2. In this presentation, we answer an open problem by determining an explicit formula for the general case k>2 by constructing an infinite family of circulant graphs for which the independence numbers can be computed explicitly. This construction gives us two further results: a new (infinite) family of star extremal graphs which are a superset of many of the families currently known in the literature, and a broad generalization of known results on the chromatic number of integer distance graphs.