Literature DB >> 26146456

STOCHASTIC SOLUTIONS FOR FRACTIONAL WAVE EQUATIONS.

Mark M Meerschaert1, René L Schilling2, Alla Sikorskii3.   

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.

Entities:  

Year:  2015        PMID: 26146456      PMCID: PMC4489163          DOI: 10.1007/s11071-014-1299-z

Source DB:  PubMed          Journal:  Nonlinear Dyn        ISSN: 0924-090X            Impact factor:   5.022


  6 in total

1.  Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency.

Authors:  W Chen; S Holm
Journal:  J Acoust Soc Am       Date:  2004-04       Impact factor: 1.840

2.  Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian.

Authors:  Bradley E Treeby; B T Cox
Journal:  J Acoust Soc Am       Date:  2010-05       Impact factor: 1.840

3.  Analytical time-domain Green's functions for power-law media.

Authors:  James F Kelly; Robert J McGough; Mark M Meerschaert
Journal:  J Acoust Soc Am       Date:  2008-11       Impact factor: 1.840

4.  Attenuated Fractional Wave Equations With Anisotropy.

Authors:  Mark M Meerschaert; Robert J McGough
Journal:  J Vib Acoust       Date:  2014-07-25       Impact factor: 1.583

5.  INVERSE STABLE SUBORDINATORS.

Authors:  Mark M Meerschaert; Peter Straka
Journal:  Math Model Nat Phenom       Date:  2013-01-01       Impact factor: 4.157

6.  Stochastic solution to a time-fractional attenuated wave equation.

Authors:  Mark M Meerschaert; Peter Straka; Yuzhen Zhou; Robert J McGough
Journal:  Nonlinear Dyn       Date:  2012-10       Impact factor: 5.022

  6 in total
  1 in total

1.  Approximate analytical time-domain Green's functions for the Caputo fractional wave equation.

Authors:  James F Kelly; Robert J McGough
Journal:  J Acoust Soc Am       Date:  2016-08       Impact factor: 1.840

  1 in total

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