Strongly LP well-posedness for abstract time-fractional Moore-Gibson-Thompson type equations

We obtain necessary and sufficient conditions for the strongly LP well-posedness of three abstract evolution equations, arising from fractional Moore-Gibson-Thompson type equations which have recently appeared in the literature. We use Fourier multiplier techniques to derive new characterizations in terms of the R-boundedness of the operator-valued symbol associated to each abstract model, when endowed with the time-fractional Liouville-Grunwald derivative. As a consequence of our characterization, we give new insights into the differences between the models based on the structure of the respective operator-valued symbols and show novel applications by including several classes of operators other than the Laplacian. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).