Fractional Crank-Nicolson Galerkin FEM for Coupled Time-Fractional Nonlocal Parabolic Problems

In this paper, we introduce a second-order numerical scheme designed for addressing a coupled time-fractional nonlocal diffusion problem. The scheme is composed of the fractional Crank-Nicolson method integrated with the Galerkin finite element method (FEM) and Newton’s method. We establish a priori error estimates for a fully-discrete solution in L2 and \(H^1_0\) norms. Additionally, we provide results based on the standard FEM to verify the theoretical estimates.