Time-fractional Moore-Gibson-Thompson equations

TL;DR

This paper introduces time-fractional generalizations of the Moore-Gibson-Thompson equations in nonlinear acoustics, deriving them from fractional Maxwell-Cattaneo laws, analyzing their well-posedness, and exploring their limits to classical equations.

Contribution

It presents novel time-fractional versions of the JMGT equations, extending the classical models and providing well-posedness results and limit analysis as fractional order approaches one.

Findings

Well-posedness of fractional JMGT equations established

Derivation from fractional Maxwell-Cattaneo laws

Limit analysis to classical third-order equations

Abstract

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. Following the procedure described in Jordan (2014), these time-fractional acoustic equations are derived from four fractional versions of the Maxwell-Cattaneo law in Compte and Metzler (1997). 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.