Numerical solution of the fractional oscillation equation by a refinable collocation method

Fractional Calculus is widely used to model real-world phenomena. In fact, the fractional derivative allows one to easily introduce into the model memory effects in time or nonlocality in space. To solve fractional differential problems efficient numerical methods are required. In this paper we solve the fractional oscillation equation by a collocation method based on refinable bases on the semi-infinite interval. We carry out some numerical tests showing the good performance of the method.