Time-fractional Moore-Gibson-Thompson equations

2021/04/28 by Barbara Kaltenbacher, Kaltenbacher, Barbara, Vanja Nikolić +1 · 1 citation
Mathematics · Physics and Astronomy · #35L05 #35L72 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2104.13967

openalex publication_date 2021/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Global existence for a fractionally damped nonlinear Jordan--Moore--Gibson--Thompson equation

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