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Time-fractional Moore-Gibson-Thompson equations

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.

preprint2022arXivOpen access
Barbara KaltenbacherVanja Nikolić
math.AP
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Barbara KaltenbacherVanja Nikolić

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