Central part interpolation schemes for a class of fractional initial value problems
Keywords:Fractional integro-differential equation, Caputo fractional derivative, weakly singular integral equation, central part interpolation, collocation method
We consider an initial value problem for linear fractional integro-differential equations with weakly singular kernels. Using an integral equation reformulation of the underlying problem, a collocation method based on the central part interpolation by continuous piecewise polynomials on the uniform grid is constructed and analysed. Optimal convergence order of the proposed method is established and confirmed by numerical experiments.