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

W. Chen, Sverre Holm

Type: Article

Publication Date: 2004-03-24

Citations: 324

DOI: https://doi.org/10.1121/1.1646399

View Publication

Locations

The Journal of the Acoustical Society of America - View
PubMed - View

Similar Works

Action	Title	Year	Authors
+	Fractional Laplacian, Levy stable distribution, and time-space models for linear and nonlinear frequency-dependent lossy media	2002	W. Chen Sverre Holm
+ PDF Chat	Fractional biharmonic operator equation model for arbitrary frequency-dependent scattering attenuation in acoustic wave propagation	2017	Wen Chen Jun Fang Guofei Pang Sverre Holm
+ PDF Chat	Variable-order fractional Laplacian and its accurate and efficient computations with meshfree methods	2024	Yixuan Wu Yanzhi Zhang
+	Accurately propagating P- and S-waves in attenuation media using spatial-independent-order decoupled fractional Laplacians	2019	Ning Wang Guangchi Xing Tieyuan Zhu
+	Physical interpretation of fractional diffusion-wave equation via lossy media obeying frequency power law	2003	W. Chen Sverre Holm
+	The Schrödinger-KdV equation of fractional order with Mittag-Leffler nonsingular kernel	2021	Mehmet Yavuz Tukur Abdulkadir Sulaıman Abdullahi Yusuf Thabet Abdeljawad
+	Two effective methods for solving nonlinear coupled time-fractional Schrödinger equations	2023	Ismail Gad Ameen Rasha Osman Ahmed Taie Hegagi Mohamed Ali
+	Modeling power law absorption and dispersion in viscoelastic solids using a split-field and the fractional Laplacian	2014	Bradley E. Treeby Ben Cox
+ PDF Chat	Nonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag-Leffler kernel	2020	Mehmet Yavuz Thabet Abdeljawad
+	A Survey on Fractional Derivative Modeling of Power-Law Frequency-Dependent Viscous Dissipative and Scattering Attenuation in Acoustic Wave Propagation	2018	Wei Cai Wen Chen Jun Fang Sverre Holm
+ PDF Chat	Modified Szabo’s wave equation models for lossy media obeying frequency power law	2003	W. Chen Sverre Holm
+ PDF Chat	Time-domain analysis of power law attenuation in space-fractional wave equations	2018	Xiaofeng Zhao Robert J. McGough
+ PDF Chat	Operational-matrix-based algorithm for differential equations of fractional order with Dirichlet boundary conditions	2019	Muhammad Usman Muhammad Hamid Tamour Zubair Rizwan Ul Haq Wei Wang
+	Meshless analysis of two-dimensional two-sided space-fractional wave equation based on improved moving least-squares approximation	2017	Rongjun Cheng Fengxin Sun Jufeng Wang
+ PDF Chat	Attenuated Fractional Wave Equations With Anisotropy	2013	Mark M. Meerschaert Robert J. McGough
+	Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations	2024	Mohsen Zayernouri Li-Lian Wang Jie Shen George Em Karniadakis
+	The approximate constant Q and linearized reflection coefficients based on the generalized fractional wave equation	2019	Fengyuan Sun Jinghuai Gao Naihao Liu
+	Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain	2024	Lifang Zhao Wei Zhang
+	A K-Space-Based Temporal Compensating Scheme for a First-Order Viscoacoustic Wave Equation with Fractional Laplace Operators	2024	Juan Chen Fei Li Ning Wang Yinfeng Wang Yang Mu Ying Shi
+	Stability analysis and conserved quantities of analytic nonlinear wave solutions in multi-dimensional fractional systems	2024	Chanyuan Wang Raghda A. M. Attia Suleman H. Alfalqi Jameel F. Alzaidi Mostafa M. A. Khater

Works That Cite This (219)

Action	Title	Year	Authors
+	A representation formula for solutions of second order ode's with time dependent coefficients and its application to model dissipative oscillations and waves	2024	Richard Kowar
+	Numerical analysis of the space fractional Navier–Stokes equations	2017	Huanying Xu Xiaoyun Jiang Bo Yu
+	A new non-standard finite difference method for analyzing the fractional Navier–Stokes equations	2018	K. Sayevand J. A. Tenreiro Machado V. Moradi
+ PDF Chat	Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation	2021	Barbara Kaltenbacher Anna Schlintl
+	Efficient numerical schemes for fractional water wave models	2015	Can Li Shan Zhao
+	On an inverse problem of nonlinear imaging with fractional damping	2021	Barbara Kaltenbacher William Rundell
+	A Numerical Scheme for Fractional Mixed Convection Flow Over Flat and Oscillatory Plates	2022	Yasir Nawaz Muhammad Shoaib Arif Kamaleldin Abodayeh
+ PDF Chat	Time–space fabric underlying anomalous diffusion	2005	W. Chen
+	Analysis of a robust implicit scheme for space–time fractional stochastic nonlinear diffusion wave model	2023	Anant Pratap Singh Rahul Kumar Maurya Vineet Kumar Singh
+	Efficient modeling of fractional Laplacian viscoacoustic wave equation with fractional finite-difference method	2024	Bingluo Gu Shanshan Zhang Xingnong Liu Jianguang Han

Works Cited by This (14)

Action	Title	Year	Authors
+	Fractional Integrals and Derivatives: Theory and Applications	1993	Stefan Samko Anatoly A. Kilbas O. I. Marichev
+	Fractional‐Derivative Maxwell Model for Viscous Dampers	1991	Nicos Makris Michael C. Constantinou
+	Representation of the absorption of nonlinear waves by fractional derivatives	1993	Martin Ochmann S. S. Makarov
+	Fractional Differentiation in the Self‐Affine Case. V ‐ The Local Degree of Differentiability	1997	Martina Zähle
+	Generalized Burgers equation for plane waves	1985	David T. Blackstock
+	A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity	1983	Ronald L. Bagley Peter J. Torvik
+	Fractional kinetic equation for Hamiltonian chaos	1994	G. M. Zaslavsky
+	Multidimensional solutions of space–fractional diffusion equations	2001	Andrzej Hanyga
+	Fractional reaction–diffusion	2000	B. I. Henry Susan L. Wearne
+	Burgers equation with a fractional derivative; hereditary effects on nonlinear acoustic waves	1991	Nobumasa Sugimoto