  We consider an integral transform introduced by Prabhakar, involving
generalised multi-parameter Mittag-Leffler functions, which can be used to
introduce and investigate several different models of fractional calculus. We
derive a new series expression for this transform, in terms of classical
Riemann-Liouville fractional integrals, and use it to obtain or verify series
formulae in various specific cases corresponding to different
fractional-calculus models. We demonstrate the power of our result by applying
the series formula to derive analogues of the product and chain rules in more
general fractional contexts. We also discuss how the Prabhakar model can be
used to explore the idea of fractional iteration in connection with semigroup
properties.
