  We investigate the properties of some recently developed variable-order
differential operators involving order transition functions of exponential
type. Since the characterisation of such operators is performed in the Laplace
domain it is necessary to resort to accurate numerical methods to derive the
corresponding behaviours in the time domain. In this regard, we develop a
computational procedure to solve variable-order fractional differential
equations of this novel class. Furthermore, we provide some numerical
experiments to show the effectiveness of the proposed techniques.
