Application of fractional calculus to ultrasonic wave propagation in human cancellous bone

Sebaa, Naima; Fellah, Zine El Abiddine; Lauriks, Walter; Dépollier, Claude

doi:10.1016/j.sigpro.2006.02.015

Cited by 89 publications

(38 citation statements)

References 13 publications

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“…The temporal operators ρ 11 (t), ρ 12 (t) et ρ 22 (t) are the operators of mass coupling between fluid and structure and are given in the high frequency range by [47]:…”

Section: Modelmentioning

confidence: 99%

Transient Acoustic Wave Propagation in Porous Media

Fellah¹,

Fellah²,

Dépollier³

2013

Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

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“…The temporal operators ρ 11 (t), ρ 12 (t) et ρ 22 (t) are the operators of mass coupling between fluid and structure and are given in the high frequency range by [47]:…”

Section: Modelmentioning

confidence: 99%

Transient Acoustic Wave Propagation in Porous Media

Fellah¹,

Fellah²,

Dépollier³

2013

Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

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“…11 The form and properties of fractional-order derivatives as mathematical description can be found in the monographs by Podlubny, 12 Herrman 13 and Meerschaert and Sikorskii, 14 while the theoretical models and experimental applications are available and published. 15 Some applications are in¯elds that include bioengineering, [16][17][18][19] lters, 20 control theory, 21 signal processing, 22 oscillators, [23][24][25][26][27][28][29] transmission lines (TLs) [30][31][32][33] and potentially many others.…”

Section: Introductionmentioning

confidence: 99%

Application of Numerical Inverse Laplace Transform Methods for Simulation of Distributed Systems with Fractional-Order Elements

R‐Smith

Kartci

Brančík

2018

J CIRCUIT SYST COMP

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The paper presents a computationally e±cient method for modeling and simulating distributed systems with lossy transmission line (TL) including multiconductor ones, by a less conventional method. The method is devised based on 1D and 2D Laplace transforms, which facilitates the possibility of incorporating fractional-order elements and frequency-dependent parameters. This process is made possible due to the development of e®ective numerical inverse Laplace transforms (NILTs) of one and two variables, 1D NILT and 2D NILT. In the paper, it is shown that in high frequency operating systems, the frequency dependencies of the system ought to be included in the model. Additionally, it is shown that incorporating fractional-order elements in the modeling of the distributed parameter systems compensates for losses along the wires, provides higher degrees of°exibility for optimization and produces more accurate and authentic modelling of such systems. The simulations are performed in the Matlab environment and are e®ectively algorithmized.

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“…In consequence, the subject of fractional differential equations is gaining much more attention. For example, in electromagnetism, Sebaa et al [3] studied ultrasonic wave propagation in human cancellous bone by using fractional calculus to describe the viscous interactions between fluid and solid structure. In signal processing, Assaleh and Ahmad [4] proposed a new approach for speech signal modeling through using fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Homotopy Series Solutions to Time-Space Fractional Coupled Systems

Zhang

Cai

Chen

et al. 2017

Discrete Dynamics in Nature and Society

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We apply the homotopy perturbation Sumudu transform method (HPSTM) to the time-space fractional coupled systems in the sense of Riemann-Liouville fractional integral and Caputo derivative. The HPSTM is a combination of Sumudu transform and homotopy perturbation method, which can be easily handled with nonlinear coupled system. We apply the method to the coupled Burgers system, the coupled KdV system, the generalized Hirota-Satsuma coupled KdV system, the coupled WBK system, and the coupled shallow water system. The simplicity and validity of the method can be shown by the applications and the numerical results.

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Application of fractional calculus to ultrasonic wave propagation in human cancellous bone

Cited by 89 publications

References 13 publications

Transient Acoustic Wave Propagation in Porous Media

Transient Acoustic Wave Propagation in Porous Media

Application of Numerical Inverse Laplace Transform Methods for Simulation of Distributed Systems with Fractional-Order Elements

Homotopy Series Solutions to Time-Space Fractional Coupled Systems

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