This work presents a brief introduction to fractional calculus and its application to some problems in rheology. We present two different viscoelastic models based on fractional derivatives (the Fractional Maxwell Model – FMM and the Fractional Viscoelastic Fluid – FVF) and discuss their reduction to the classical Newtonian and Maxwell fluids. A third model is also studied (an extension of the FMM to an invariant form), being given by a combination of the K-BKZ integral model with a fractional memory function which we denote the Fractional K-BKZ model. We discuss and illustrate the ability of these models to fit experimental data, and present numerical results for simple stress relaxation following step strain and steady shearing.
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