We consider the fractional-order version of the hybrid integrator-gain system (HIGS) including memory reset. For the implementation an explicit higher-order approximation is considered, which combines first-order reset elements with an integer-order HIGS. This framework can also be used for fractional-order extensions without memory reset. Using passivity theory we present a Circle-Criterion-like condition for the closed-loop stability based on this higher-order approximation.