Closed String Radiation from the Interacting Fractional-Dressed D$p$-Branes with the Transverse Motions

We determine the boundary states, associated with a fractional D$p$-brane in the presence of the Kalb-Ramond field and a $U(1)$ gauge potential. The background spacetime is the non-compact orbifold ${\mathbb{R}}^{1,21}\otimes {\mathbb{R}}^4\mathrm{/}{\mathbb{Z}}_2$. Besides, the brane has a transverse velocity. We compute the radiation amplitude of a massless closed string from the interaction of two fractional D$p$-branes with the previous background fields. The branes have been dressed by different fields and have transverse motions. The total radiation amplitude will be investigated for large inter-brane separation. Finally, the graviton, Kalb-Ramond (axion) and dilaton emissions will be distinctly studied. Our calculations are in the context of the bosonic string theory.