A one-dimensional fractional diffusion model is considered, where the usual second order derivative gives place to a fractional derivative of order α, with 1<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. © 2011 Elsevier Ltd. All rights reserved.
Sousa, E. (2011). Numerical approximations for fractional diffusion equations via splines. Computers and Mathematics with Applications, 62(3), 938–944. https://doi.org/10.1016/j.camwa.2011.04.015