New discretization of Caputo-Fabrizio derivative

Abstract

We derive a numerical approximation, namely L1-2 formula, to the Caputo-Fabrizio derivative by using a quadratic interpolation. Quadratic and cubic convergence rates are achieved for L1 and L1-2 formulas using Lagrange interpolation, respectively. We compute Caputo-Fabrizio derivatives of some known functions both theoretically and numerically. In addition, we solve non/linear sub-diffusion equations to test theoretical findings. Numerical results confirm the theoretically observed convergence rates.