The statistics of interspike intervals is one of the principle characteristics of the synaptic activity of neurons. This statistics can be presented with the values of the moments of these intervals. For the integrate-and-fire type models, the formalism of first passage time provides partial differential equations for a rigorous calculation of these values for neurons subject to a white Gaussian noise. However, the procedure of derivation of these equations is quite sophisticated and the results for Gaussian noise are not as trivial as they can appear if one does not look at the rigorous derivation procedure. The derivation of analogous partial differential equations for the case of alpha-stable (Lévy) noise is even more involved. In this paper, the equations providing moments of interspike intervals are derived for quadratic integrate-and-fire neurons subject to symmetric alphastable noise. The results are presumably generalizable to other integrate-and-fire type models (e.g., leakage ones). The paper was presented at the 11th International Scientific Conference on Physics and Control (PhysCon 2024), September 9–12, 2024, Istanbul, Turkey.