  In this paper, the numerical approximation of the generalized Burgers'-Huxley
equation (GBHE) with weakly singular kernels using non-conforming methods will
be presented. Specifically, we discuss two new formulations. The first
formulation is based on the non-conforming finite element method (NCFEM). The
other formulation is based on discontinuous Galerkin finite element methods
(DGFEM). The wellposedness results for both formulations are proved.
  Then, a priori error estimates for both the semi-discrete and fully-discrete
schemes are derived.
  Specific numerical examples, including some applications for the GBHE with
weakly singular model, are discussed to validate the theoretical results.
