  We shall construct two boundary states which are corresponding to a dynamical
fractional D$p$-brane in the presence of the fluxes of the Kalb-Ramond field
and a $U(1)$ gauge potential, in the partially orbifold spacetime
$\mathbb{R}^{1, 5}\times\mathbb{C}^{2}/\mathbb{Z}_{2}$. These states accurately
describe the D$p$-brane in the twisted and untwisted sectors under the orbifold
projection. We use them to compute the interaction of two parallel fractional
D$p$-branes with the transverse velocities, tangential rotations and tangential
linear motions. Various properties of the interaction, such as its long-range
force, will be discussed.
