In computational neuroscience, it is of crucial importance to dispose of a model that is able to accurately describe the single-neuron activity. This model should be at the same time biologically relevant and computationally fast. Many different phenomenological models have been proposed. In particular, the adaptive exponential integrate-and-fire model (AdEX) introduced by R. Brette and W. Gerstner accounts for adaptation via spike-triggered currents and the dynamical threshold introduced by Badel et al. Includes refractoriness via a dynamical threshold. In real neurons, adaptation occurs on multiple timescales. Furthermore, it has also been shown that the dynamics of the adaptation depends on the timescale on which the input statistics varies. Here, a new model is proposed that combines both adaptation and refractoriness. In practice, a slightly modified version of the AdEX model was extended using different dynamics of the voltage threshold. To account for multiple-timescale adaptation, power law dynamics was considered. It was also investigated whether the ability to predict spike timing could be improved by driving the modified AdEX model with the fractional derivative of the injected current. All the proposed models were fitted on experimental data from rat cortical pyramidal neurons. The models proposed here can reproduce the activity of the real neuron with high accuracy and about 60% of the observed spikes were correctly predicted with a precision of ±3ms. The introduction of a moving threshold did not not improve in a drastic way the ability to predict spikes, but in the case of cumulative power law dynamics the model was able to capture scale-invariant adaptation. It turns out that the fractional derivative of the injected current can partially account for adaptation. However, the best model takes as input signal the injected current and has both cumulative power law threshold and spike-triggered current