  For two-dimensional autonomous linear incommensurate fractional-order
dynamical systems with Caputo derivatives of different orders, necessary and
sufficient conditions are obtained for the asymptotic stability and instability
of the null solution. These conditions are expressed in terms of the elements
of the system's matrix, as well as of the fractional orders of the Caputo
derivatives, leading to a generalization of the well known Routh-Hurwitz
conditions. These theoretical results are then used to investigate the
stability properties of a two-dimensional fractional-order FitzHugh-Nagumo
neuronal model. The occurrence of Hopf bifurcations is also discussed.
Numerical simulations are provided with the aim of exemplifying the theoretical
results, revealing rich spiking behavior, in comparison with the classical
integer-order FitzHugh-Nagumo model.
