STOCHASTIC SOLUTIONS FOR FRACTIONAL WAVE EQUATIONS

Nonlinear Dyn. 2015 Jun 1;80(4):1685-1695. doi: 10.1007/s11071-014-1299-z.

Abstract

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.