  This paper presents a novel First Order Plus Fractional Diffusive Delay
(FOPFDD) model, capable of modeling delay dominant systems with high accuracy.
The novelty of the FOPFDD is the Fractional Diffusive Delay (FDD) term, an
exponential delay of non-integer order $\alpha$, i.e. $e^{-(Ls)^{\alpha}}$ in
Laplace domain. The special cases of $\alpha = 0.5$ and $\alpha = 1$ have
already been investigated thoroughly. In this work $\alpha$ is generalized to
any real number in the interval $]0,1[$. For $\alpha=0.5$, this term appears in
the solution of distributed diffusion systems, which will serve as a source of
inspiration for this work. Both frequency and time domain are investigated.
However, regarding the latter, no closed-form expression of the inverse Laplace
transform of the FDD can be found for all $\alpha$, so numerical tools are used
to obtain an impulse response of the FDD. To establish the algorithm, several
properties of the FDD term have been proven: firstly, existence of the term,
secondly, invariance of the time integral of the impulse response, and thirdly,
dependency of the impulse response's energy on $\alpha$. To conclude, the
FOPFDD model is fitted to several delay-dominant, diffusive-like
resistors-capacitors (RC) circuits to show the increased modeling accuracy
compared to other state-of-the-art models found in literature. The FOPFDD model
outperforms the other approximation models in accurately tracking frequency
response functions as well as in mimicing the peculiar delay/diffusive-like
time responses, coming from the interconnection of a large number of discrete
subsystems. The fractional character of the FOPFDD makes it an ideal candidate
for an approximate model to these large and complex systems with only a few
parameters.
