  In this paper, we consider several time-fractional generalizations of the
Jordan-Moore-Gibson-Thompson (JMGT) equations in nonlinear acoustics as well as
their linear Moore-Gibson-Thompson (MGT) versions. Additionally to providing
well-posedness results for each of them, we also study the respective limits as
the fractional order tends to one, leading to the classical third order in time
(J)MGT equation.
