Could acceleration of a pulsar affect braking index?

In the coming era of multi-messenger astrophysics, pulsars might be one of the most possible electromagnetic counterparts of the gravitational wave. The braking indices, which are related closely to the electromagnetic radiation of pulsars, are shown to be larger for the pulsars with companion. It motivates us to set up a modified spin-down equation for accelerated pulsars. In this model, we attempt to figure out whether acceleration of a pulsar can cause a larger braking index