Implement quadrature 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 3: Riemann-Liouville quadrature
  • ✔️ 3.1.I: Fractional rectangular rule
  • ✔️ 3.1.II: Fractional trapezoidal rule
  • ✔️ 3.1.III: Fractional Simpson's rule
  • ❌ 3.1.IV: Fractional Newton-Cotes rules
  • ❔ 3.1.V: Cubic Hermitian interpolation rules
  • ❔ 3.2: Fractional multistep methods
  • ✔️ 3.3.I: Spectral approximations with Jacobi polynomials
  • ❔ 3.3.II: Spectral approximations with Legendre polynomials
    • Already works for Jacobi with $\alpha = \beta = 0$.
  • ❔ 3.3.III: Spectral approximations with Chebyshev polynomials
    • Already works for Jacobi with $\alpha = \beta = -1/2$.
  • ❔ 3.4: Diffusive approximations

[alexfikl]

Generic Newton-Cotes is quite hard to implement (Li2020 doesn't give any details) since we can't nicely integrate arbitrary order Lagrange polynomials.