  Necessary and sufficient conditions are given for the asymptotic stability
and instability of a two-dimensional incommensurate order autonomous linear
system, which consists of a differential equation with a Caputo-type fractional
order derivative and a classical first order differential equation. These
conditions are expressed in terms of the elements of the system's matrix, as
well as of the fractional order of the Caputo derivative. In this setting, we
obtain a generalization of the well known Routh-Hurwitz conditions. These
theoretical results are then applied to the analysis of a two-dimensional
fractional-order Morris-Lecar neuronal model, focusing on stability and
instability properties. This fractional order model is built up taking into
account the dimensional consistency of the resulting system of differential
equations. The occurrence of Hopf bifurcations is also discussed. Numerical
simulations exemplify the theoretical results, revealing rich spiking behavior.
The obtained results are also compared to similar ones obtained for the
classical integer-order Morris-Lecar neuronal model.
