Generalized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations

In this paper, we present a generalized Jacobi spectral Galerkin method for fractional Volterra integro-differential equations (FVIDEs). The basis functions of the proposed method are generalized Jacobi functions, which serve as natural basis functions for appropriately designed spectral methods for FVIDEs. We establish a convergence analysis of the generalized Jacobi spectral Galerkin method under reasonable assumptions. Numerical experiments are provided to demonstrate the effectiveness of the proposed method.