Implement derivative methods from Li2020

[alexfikl]

Li2020 contains a fairly up to date set of numerical methods for fractional derivatives and integrals.
It would be very cool to implement most of this and compare.

• Chapter 4: Caputo differentiation

  • ✔️ 4.1.1: L1 method
  • ✔️ 4.1.2.I: L2 method
  • ✔️ 4.1.2.II: L2C method
  • ❔ 4.2.1: $3 - \alpha$ order approximation
  • ❔ 4.2.2: $4 - \alpha$ order approximation
  • ❔ 4.2.3: $r + 1 - \alpha$ order approximation
  • ❔ 4.2.4: Spline interpolation
  • ❔ 4.3: Fractional linear multistep method
  • ✔️ 4.4: Spectral approximations
  • ❔ 4.5: Diffusive approximation

• Chapter 5: Riemann-Liouville differentiation

  • ✔️ 5.1: L1, L2, L2C methods
  • ❔ 5.2: Spline interpolation
  • ❔ 5.3.1: Classical Grünwald-Letnikov formula
  • ❔ 5.3.2: Shifted Grünwald-Letnikov formula
  • ❔ 5.3.3: Weighted and shifted Grünwald-Letnikov formula
  • ❔ 5.4.1: Classical Lubich formula
  • ❔ 5.4.2: Shifted fractional backward difference formula
  • ❔ 5.4.3: Weighted and shifted Lubich formula
  • ❔ 5.4.4: Fractional-compact formula
  • ❔ 5.5: Fractional average central difference method
  • ❔ 5.6: Spectral approximations
  • ❔ 5.7: Numerical method based on finite-part integrals