Numerical methods for fractional-order models of viscoelastic materials

The dynamics of many classes of materials may be well modeled by fractional-order differential equations. As a matter of fact, the memory effect of the fractional derivative allows to catch some peculiarities of viscoelastic materials. Besides, the dynamics in fractal and non-local media can be effectively described by fractional models. The analytical solution of such models usually is not available or expensive to compute. Therefore, an accurate and efficient numerical simulation is necessary in scientific applications. Here we propose a numerical approach based on spline collocation. The theoretical analysis of the error and the experimental validation prove that spline collocation methods provide a reliable numerical approximation, at a reasonable computational cost.