On exact and discretized stability of a linear fractional delay differential equation (Q1985387)

The authors discuss the exact and discretized stability of a linear functional delay differential equation. The basic stability criterion to test one-term fractional delay differential equation with a complex coefficient is given. Some definitions, Laplace transform and boundary locus technique are introduced. A fractional analogue of the Levin-May stability condition from the area of discrete population dynamics is presented. In addition, the authors point out that contrary to the integer-order case the backward Euler discretization of the underlying fractional delay differential equations is not \(\tau\)-stable.