Stochastic solutions for fractional wave equations

Stochastic solutions for fractional wave equations

A fractional wave equation replaces the second time derivative by a Caputo derivative of order between one and two. In this paper, we show that the fractional wave equation governs a stochastic model for wave propagation, with deterministic time replaced by the inverse of a stable subordinator whose...

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Veröffentlicht in:Nonlinear dynamics 2015-06, Vol.80 (4), p.1685-1695
Hauptverfasser: Meerschaert, Mark M., Schilling, René L., Sikorskii, Alla
Format: Artikel
Sprache:eng
Schlagworte:
Automotive Engineering
Classical Mechanics
Control
Derivatives
Dynamical Systems
Engineering
Inverse
Mathematical models
Mechanical Engineering
Nonlinear dynamics
Original Paper
Stochastic models
Stochasticity
Vibration
Wave equations
Wave propagation
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Beschreibung
Zusammenfassung:A fractional wave equation replaces the second time derivative by a Caputo derivative of order between one and two. In this paper, we show that the fractional wave equation governs a stochastic model for wave propagation, with deterministic time replaced by the inverse of a stable subordinator whose index is one-half the order of the fractional time derivative.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-014-1299-z