The current manuscript examines the effect of the fractional temporal variation on the
vibration of waves on non-homogeneous elastic substrates by applying the Laplace integral
transform and the asymptotic approach. Four different non-homogeneities, including linear
and exponential forms, are considered and scrutinized. In the end, it is reported that the
fractional temporal variation significantly affects the respective vibrational fields greatly as
the vibrations increase with a decrease in the fractional-order µ. Besides, the two …