  Diffusive representations of fractional differential and integral operators
can provide a convenient means to construct efficient numerical algorithms for
their approximate evaluation. In the current literature, many different
variants of such representations have been proposed. Concentrating on
Riemann-Liouville integrals whose order is in (0,1), we here present a general
approach that comprises most of these variants as special cases and that allows
a detailed investigation of the analytic properties of each variant. The
availability of this information allows to choose concrete numerical methods
for handling the representations that exploit the specific properties, thus
allowing to construct very efficient overall methods.
