In this paper, we studied the geodesics of timelike and null like particles
near an improved Schwarzschild black hole. The lapse function has been plotted
and was found that only one horizon is possible. The equation of motion and
effective potential of test particle have been calculated. This equation has an
importance in studying the radial free fall and in studying the stability of
radial orbits (trajectories). The energy and angular momentum have also been
calculated to analysis the cicrular motion and stability of circular orbits.
Moreover, Innermost stable circular orbit radius has determined. To get a
deeper insight of the nature of these trajectories, we have studied the
timelike and null geodesics with the help of the dynamical systems approach.
This analysis help us to determine the stability as well as fixed point of
phase space trajectories.