Calculation of giant fractional Shapiro steps in Josephson-junction arrays

We calculate the rsponse of an N×N array of resistively shunted Josephson junctions to an imposed current I=${\mathit{I}}_{\mathrm{dc}}$+${\mathit{I}}_{\mathrm{ac}}$sin(2πνt). In a transverse dc magnetic field of p/q==f flux quanta per plaquette of area, we find fractional giant Shapiro steps in the time-averaged voltage 〈V〉 at values 〈V〉=nNhν/2eq, n=1,2,3,..., in agreement with the measurements of Benz et al. At f=1/5, 2/5, and 1/3, we find additional fractional steps at 〈V〉=Nhν/(4e). A generalization of the model of Benz et al. accounts for both the fractional giant steps at p/q and the anomalous half-integer steps.