  The family of Jordan-Moore-Gibson-Thompson (JMGT) equations arises in
nonlinear acoustics when a relaxed version of the heat flux law is employed
within the system of governing equations of sound motion. Motivated by the
propagation of sound waves in complex media with anomalous diffusion, we
consider here a generalized class of such equations involving two (weakly)
singular memory kernels in the principal and non-leading terms. To relate them
to the second-order wave equations, we investigate their vanishing relaxation
time behavior. The key component of this singular limit analysis are the
uniform bounds for the solutions of these nonlinear equations of fractional
type with respect to the relaxation time. Their availability turns out to
depend not only on the regularity and coercivity properties of the two kernels,
but also on their behavior relative to each other and the type of nonlinearity
present in the equations.
