  To capture specific characteristics of non-Newtonian fluids, during the past
years fractional constitutive models have become increasingly popular. These
models are able to capture in a simple and compact way the complex behaviour of
viscoelastic materials, such as the change in power-law relaxation pattern
during the relaxation process of some materials. Using the Lagrangian
Smoothed-Particle Hydrodynamics (SPH) method we can easily track particle
history; this allows us to solve integral constitutive models in a novel way,
without relying on complex tasks. Hence, we develop here a SPH integral
viscoelastic method which is first validated for simple Maxwell or Oldroyd-B
models under Small Amplitude Oscillatory Shear flows (SAOS). By exploiting the
structure of the integral method, a multi-mode Maxwell model is then
implemented. Finally, the method is extended to include fractional constitutive
models, validating the approach by comparing results with theory under SAOS.
