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In this article we propose a scheme for solving the coupled time-fractionalnonlocal diffusion problem. The scheme consist of fractional Crank-Nicolsonmethod with Galerkin finite element method (FEM) and Newton's method. We derive\emph{a priori} error estimates for fully-discrete solutions in $L^2$ and$H^1_0$ norms. Results based on the usual finite element method are provided toconfirm the theoretical estimates.

Fractional Crank-Nicolson Galerkin finite element analysis for coupled time-fractional nonlocal parabolic problem