  Interval approaches for the reachability analysis of initial value problems
for sets of classical ordinary differential equations have been investigated
and implemented by many researchers during the last decades. However, there
exist numerous applications in computational science and engineering, where
continuous-time system dynamics cannot be described adequately by integer-order
differential equations. Especially in cases in which long-term memory effects
are observed, fractional-order system representations are promising to describe
the dynamics, on the one hand, with sufficient accuracy and, on the other hand,
to limit the number of required state variables and parameters to a reasonable
amount. Real-life applications for such fractional-order models can, among
others, be found in the field of electrochemistry, where methods for impedance
spectroscopy are typically used to identify fractional-order models for the
charging/discharging behavior of batteries or for the dynamic relation between
voltage and current in fuel cell systems if operated in a non-stationary state.
This paper aims at presenting an iterative method for reachability analysis of
fractional-order systems that is based on an interval arithmetic extension of
Mittag-Leffler functions. An illustrating example, inspired by a low-order
model of battery systems concludes this contribution.
