  We show that an introduction of a phase parameter ($\alpha$), with $0 \le
\alpha \le \pi/2$, in the interlayer coupling terms of multiplex networks of
Kuramoto oscillators can induce explosive synchronization (ES) in the
multiplexed layers. Along with the {\alpha} values, the hysteresis width is
determined by the interlayer coupling strength and the frequency mismatch
between the mirror (inter-connected) nodes. A mean-field analysis is performed
to support the numerical results. Similar to the earlier works, we find that
the suppression of synchronization is accountable for the origin of ES. The
robustness of ES against changes in the network topology and frequency
distribution is tested. Finally, taking a suggestion from the synchronized
state of the multiplex networks, we extend the results to the classical concept
of the single-layer networks in which some specific links are assigned a
phase-shifted coupling. Different methods have been introduced in the past
years to incite ES in coupled oscillators; our results indicate that a
phase-shifted coupling can also be one such method to achieve ES.
