Consider fractional-derivative two-point boundary value problems where the leading term in the differential operator is either a Riemann-Liouville or a Caputo derivative of order 2-δ with 0 <δ< 1.Each class of problem is reformulated in terms of weakly singular Volterra integral equations.Existence and uniqueness of the solution is proved and an efficient collocation method that uses piecewise polynomials of arbitrary order on a graded mesh is analysed.This is joint work with Natalia Kopteva.