  In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac
equation on a gravitational background within the generalized uncertainty
principle. We have shown that how minimal length parameters effect the Dirac
particle in a spacetime described by conformally flat metric. Also,
supersymmetric quantum mechanics is used both to factorize the Dirac
Hamiltonians and obtain new metric functions. Finally, it is observed that the
energy dependent potentials may be extended to the energy dependent metric
functions.
