Spectral Collocation Methods for Fractional Integro-Differential Equations with Weakly Singular Kernels

In this paper, we propose and analyze a spectral approximation for the numerical solutions of fractional integro-differential equations with weakly kernels. First, original are transformed into an equivalent singular Volterra integral equation, which possesses nonsmooth solutions. To eliminate singularity solution, introduce some suitable smoothing transformations, then use Jacobi collocation method to approximate resulting equation. Later, accuracy proposed is investigated in infinity norm weighted L 2 norm. Finally, examples considered verify obtained theoretical results.