Abstract
A two-point boundary value problem whose highest order term is a Riemann–Liouville fractional derivative of order 2−δ with 0<δ<1 is considered. Such problem is reformulated as a Volterra integral equation of the second kind. An integral discrete scheme is developed for this Volterra integral equation on an adaptive grid that is constructed adaptively from a knowledge of the exact solution. It is shown from a rigorous priori error analysis that the discrete solutions are uniformly convergent with respect to the parameter δ. Besides, in order to establish the parameter of the Volterra integral equation, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of presented method.
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