  In this study, we consider a class of non-autonomous time-fractional partial
advection-diffusion-reaction (TF-ADR) equations with Caputo type fractional
derivative. To obtain the numerical solution of the model problem, we apply the
non-symmetric interior penalty Galerkin (NIPG) method in space on a uniform
mesh and the L1-scheme in time on a graded mesh. It is demonstrated that the
computed solution is discretely stable. Superconvergence of error estimates for
the proposed method are obtained using the discrete energy-norm. Also, we have
applied the proposed method to solve semilinear problems after linearizing by
the Newton linearization process. The theoretical results are verified through
numerical experiments.
