  Diffusive representations of fractional derivatives have proven to be useful
tools in the construction of fast and memory efficient numerical methods for
solving fractional differential equations. A common challenge in many of the
known variants of this approach is that they require the numerical
approximation of some integrals over an unbounded integral whose integrand
decays rather slowly which implies that their numerical handling is difficult
and costly. We present a novel variant of such a diffusive representation. This
form also requires the numerical approximation of an integral over an unbounded
domain, but the integrand decays much faster. This allows to use well
established quadrature rules with much better convergence properties.

Numerical Analysis;Numerical Analysis