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Diffusive representations of fractional derivatives have proven to be usefultools in the construction of fast and memory efficient numerical methods forsolving fractional differential equations. A common challenge in many of theknown variants of this approach is that they require the numericalapproximation of some integrals over an unbounded integral whose integranddecays rather slowly which implies that their numerical handling is difficultand costly. We present a novel variant of such a diffusive representation. Thisform also requires the numerical approximation of an integral over an unboundeddomain, but the integrand decays much faster. This allows to use wellestablished quadrature rules with much better convergence properties.

A New Diffusive Representation for Fractional Derivatives and its Application