  In the framework of the Dirac-Bogoliubov-de Gennes formalism, we investigate
the transport properties in the surface of a 3-dimensional topological
insulator-based hybrid structure, where the ferromagnetic and superconducting
orders are simultaneously induced to the surface states via the proximity
effect. The superconductor gap is taken to be spin-singlet $d$-wave symmetry.
The asymmetric role of this gap respect to the electron-hole exchange, in one
hand, affects the topological insulator superconducting binding excitations
and, on the other hand, gives rise to forming distinct Majorana bound states at
the ferromagnet/superconductor interface. We propose a topological insulator
N/F/FS junction and proceed to clarify the role of $d$-wave asymmetry pairing
in the resulting subgap and overgap tunneling conductance. The perpendicular
component of magnetizations in F and FS regions can be at the parallel and
antiparallel configurations leading to capture the experimentally important
magnetoresistance (MR) of junction. It is found that the zero-bias conductance
is strongly sensitive to the magnitude of magnetization in FS region $m_{zfs}$
and orbital rotated angle $\alpha$ of superconductor gap. The negative MR only
occurs in zero orbital rotated angle. This result can pave the way to
distinguish the unconventional superconducting state in the relating
topological insulator hybrid structures.
