  This paper presents a method for structural identifiability analysis of
fractional order systems by using the coefficient mapping concept to determine
whether the model parameters can uniquely be identified from input-output data.
The proposed method is applicable to general non-commensurate fractional order
models. Examples are chosen from battery fractional order equivalent circuit
models (FO-ECMs). The battery FO-ECM consists of a series of parallel resistors
and constant phase elements (CPEs) with fractional derivatives appearing in the
CPEs. The FO-ECM is non-commensurate if more than one CPE is considered in the
model. Currently, estimation of battery FO-ECMs is performed mainly by fitting
in the frequency domain, requiring costly electrochemical impedance
spectroscopy equipment. This paper aims to analyse the structural
identifiability of battery FO-ECMs directly in the time domain. It is shown
that FO-ECMs with finite numbers of CPEs are structurally identifiable. In
particular, the FO-ECM with a single CPE is structurally globally identifiable.
