Numerical approximations for fractional diffusion equations via splines

A one-dimensional fractional diffusion model is considered, where the usual second order derivative gives place to a fractional derivative of order αα, with 1<α≤21<α≤2. We consider the Caputo derivative as the space derivative, which is a form of representing the fractional derivative by an integral operator. An implicit numerical method is derived which uses a spline approximation for the Caputo derivative. The consistency and stability of the method are examined and numerical results are presented.