Numerical solution of linear fractional weakly singular integro-differential equations with integral boundary conditions

We consider a class of boundary value problems for linear fractional weakly singular integro-differential equations with Caputo fractional derivatives and integral boundary conditions. Using an integral equation reformulation of the boundary value problem, we first study the regularity of the exact solution and its Caputo derivative. Based on the obtained regularity properties and by using suitable smoothing transformations along with spline collocation techniques, the numerical solution of the problem is discussed. Optimal global convergence estimates are derived and a superconvergence result for a special choice of grid and collocation parameters is given. A numerical illustration is also presented. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.