  Fast radio bursts (FRBs) are transient intense radio pulses with duration of
milliseconds. Although the first FRB was detected more than a decade ago, the
progenitors of these energetic events are not yet known. The currently
preferred formation channel involves the formation of a neutron star
(NS)/magnetar. While these objects are often the end product of the
core-collapse (CC) explosion of massive stars, they could also be the outcome
of the merging of two massive white dwarfs. In the merger scenario the ejected
material interacts with a constant-density circumbinary medium and creates
supersonic shocks. We found that when a radio pulse passes through these shocks
the dispersion measure (DM) increases with time during the free expansion
phase. The rotation measure (RM) displays a similar trend if the power-law
index, $n$, of the outer part of the ejecta is $>6$. For $n = 6$ the RM remains
constant during this phase. Later, when the ejecta move into the Sedov-Taylor
phase while the DM still increases, however, with a different rate, the RM
reduces. This behaviour is somewhat similar to that of FRB 121102 for which a
marginal increase of DM and a 10% decrease of RM have been observed over time.
These features are in contrast to the CC scenario, where the DM and RM
contributions to the radio signal always diminish with time.
