In this work we employ integer- and fractional-order viscoelastic models in a one-dimensional blood flow solver, and study their behavior by presenting an in-silico study on a large patient-specific cranial network. The use of fractional-order models is motivated by recent experimental studies indicating that such models provide a new flexible alternative to fitting biological tissue data. This is attributed to their inherent ability to control the interplay between elastic energy storage and viscous dissipation by tuning a single parameter, the fractional order α, as well as to account for a continuous viscoelastic relaxation spectrum. We perform simulations using four viscoelastic parameter data-sets aiming to compare different viscoelastic models and highlight the important role played by the fractional order. Moreover, we carry out a detailed global stochastic sensitivity analysis study to quantify uncertainties of the input parameters that define each wall model. Our results confirm that the effect of fractional models on hemodynamics is primarily controlled by the fractional order, which affects pressure wave propagation by introducing viscoelastic dissipation in the system.