  A two-point boundary value problem whose highest-order term is a Caputo
fractional derivative of order $\delta \in (1,2)$ is considered. Al-Refai's
comparison principle is improved and modified to fit our problem. Sharp a
priori bounds on derivatives of the solution $u$ of the boundary value problem
are established, showing that $u''(x)$ may be unbounded at the interval
endpoint $x=0$. These bounds and a discrete comparison principle are used to
prove pointwise convergence of a finite difference method for the problem,
where the convective term is discretized using simple upwinding to yield
stability on coarse meshes for all values of $\delta$. Numerical results are
presented to illustrate the performance of the method.
