  The medium modifications of the open charm mesons ($D$ and $\bar D$) are
studied in isospin asymmetric nuclear matter in the presence of strong magnetic
fields, using a chiral effective model. The mass modifications of these mesons
in the effective hadronic model, arise due to their interactions with the
protons, neutrons and the scalar mesons (non-strange isoscalar $\sigma$,
strange isoscalar, $\zeta$ and non-strange isovector, $\delta$), in the
magnetized nuclear matter. In the presence of magnetic field, for the charged
baryon, i.e., the proton, the number density as well as the scalar density have
contributions due to the summation over the Landau energy levels. For a given
value of the baryon density, $\rho_B$, and isospin asymmetry, the scalar fields
are solved self consistently from their coupled equations of motion. The
modifications of the masses of the $D$ and $\bar D$ mesons are calculated, from
the medium modifications of the scalar fields and the nucleons. The effects of
the anomalous magnetic moments of the nucleons on the masses of the open charm
mesons are also investigated in the present work. The effects of isospin
asymmetry as well as of the anomalous magnetic moments are observed to be
prominent at high densities for large values of magnetic fields.
