  The solution of time fractional partial differential equations in general
exhibit a weak singularity near the initial time. In this article we propose a
method for solving time fractional diffusion equation with nonlocal diffusion
term. The proposed method comprises L1 scheme on graded mesh, finite element
method and Newton's method. We discuss the well-posedness of the weak
formulation at discrete level and derive \emph{a priori} error estimates for
fully-discrete formulation in $L^2(\Omega)$ and $H^1(\Omega)$ norms. Finally,
some numerical experiments are conducted to validate the theoretical findings.
