Time-fractional Moore–Gibson–Thompson equations
Barbara Kaltenbacher, Vanja Nikolić
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.
Topics & Concepts
MathematicsNonlinear systemOrder (exchange)Fractional calculusMathematical analysisApplied mathematicsCalculus (dental)Mathematical physicsPhysicsMedicineDentistryFinanceQuantum mechanicsEconomicsFractional Differential Equations SolutionsNonlinear Waves and SolitonsNumerical methods in engineering