When a linear controller is replaced by a reset controller, it is possible to keep the gain behaviour essentially the same, while improving the phase behaviour. However, because reset control is nonlinear, higher order harmonics appear, which may deteriorate the results. In this paper, reset controllers are combined with fractional derivatives, decreasing the magnitude of higher order harmonics. In this way, better results are found in simulations of a Clegg integrator, of a FORE (first order reset element), and of a CgLp (constant in gain lead in phase) controller. The reason why better results are found is explained.