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 |
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| container_title | Nonlinear dynamics |
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| creator | Meerschaert, Mark M. Schilling, René L. Sikorskii, Alla |
| description | 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. |
| doi_str_mv | 10.1007/s11071-014-1299-z |
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| ispartof | Nonlinear dynamics, 2015-06, Vol.80 (4), p.1685-1695 |
| issn | 0924-090X 1573-269X |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | 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 |
| title | Stochastic solutions for fractional wave equations |
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