Generalized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations with Weakly Singular Kernels

Abstract

For fractional Volterra integro-differential equations (FVIDEs) with weakly singular kernels, this paper proposes a generalized Jacobi spectral Galerkin method. The basis functions for the provided method are selected generalized Jacobi functions (GJFs), which can be utilized as natural basis functions of spectral methods for weakly singular FVIDEs when appropriately constructed. The developed method’s spectral rate of convergence is determined using the L ∞ -norm and the weighted L 2 -norm. Numerical results indicate the usefulness of the proposed method.