Approximation of the Riesz–Caputo Derivative by Cubic Splines

Differential problems with the Riesz derivative in space are widely used to model anomalous diffusion. Although Riesz–Caputo is more suitable for modeling real phenomena, there few examples literature where numerical methods solve such differential problems. In this paper, we propose approximate of a given function cubic spline. As far as aware, first time that splines have been context derivative. To show effectiveness proposed method, present tests which compare analytical solution several boundary obtain by spline collocation method. The results method efficient and accurate.