Spline Collocation for Multi-Term Fractional Integro-Differential Equations with Weakly Singular Kernels - Pedas, Arvet; Vikerpuur, Mikk (Fractal and fractional, 2021)
We consider general linear multi-term Caputo fractional integro-differential equations with weakly singular kernels subject to local or non-local boundary conditions. Using an integral equation reformulation of the proposed problem, we first study the existence, uniqueness and regularity of the exact solution. Based on the obtained regularity properties and 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.