Solving non-Hermitian Dirac equation in the presence of PDM and local Fermi velocity

We present a new approach to study class of non-Hermitian (1+1)-dimensional Dirac Hamiltonian in the presence local Fermi velocity. apply well known Nikiforov-Uvarov method solve such system. discuss applications and explore solvability both $\mathcal{PT}$-symmetric non-$\mathcal{PT}$ symmetric classes potentials. In former case we obtain solution harmonic oscillator linear vector potential while latter shifted problem.