Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas

Liu, Quansheng; Chen, Liguo

doi:10.1155/2020/9075823

Cited by 15 publications

(18 citation statements)

References 44 publications

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“…And set Q � − 0.01, C 1 � 0.1, and C 3 � − 500. erefore, by using (21), we obtain the coefficients of (36) as follows:…”

Section: Analysis and Discussionmentioning

confidence: 99%

“…Fractional derivative theory and methods [15][16][17][18] are widely used in the study of nonequilibrium systems of various intermediate processes and critical phenomena in physics and mechanics, especially in nonlinear science [19][20][21][22]. Fractional differential equations are transformed in a standard differential equation by replacing the time derivative or the space derivative with the fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

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Modelling and Analysis of Complex Viscous Fluid in Thin Elastic Tubes

Gao

Zhang

2020

Complexity

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Cardiovascular disease is a major threat to human health. The study on the pathogenesis and prevention of cardiovascular disease has received special attention. In this paper, we have contributed to the derivation of a mathematical model for the nonlinear waves in an artery. From the Navier–Stokes equations and continuity equation, the vorticity equation satisfied by the blood flow is established. And based on the multiscale analysis and perturbation method, a new model of the Boussinesq equation with viscous term is derived to describe the propagation of a viscous fluid through a thin tube. In order to be more consistent with the flow of the fluid, the time-fractional Boussinesq equation with viscous term is deduced by employing the semi-inverse method and the fractional variational principle. Moreover, the approximate analytical solution of the fractional equation is obtained, and the effect of viscosity on the amplitude and width of the wave is studied. Finally, the effects of the fractional order parameters and vessel radius on blood flow volume are discussed and analyzed.

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“…And set Q � − 0.01, C 1 � 0.1, and C 3 � − 500. erefore, by using (21), we obtain the coefficients of (36) as follows:…”

Section: Analysis and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling and Analysis of Complex Viscous Fluid in Thin Elastic Tubes

Gao

Zhang

2020

Complexity

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“…In 2014, Fujioka et al [17] described fractional optical solitons by an extended NLS equation with fractional dispersion and fractional nonlinearity. In 2020, Liu and Chen [31] derived the timespace fractional cylindrical Kadomtsev-Petviashvili (cKP) and modified cKP equations which better described the propagation of ion-acoustic waves in ultrarelativistic plasmas. In order to fully understand the propagation characteristics and periodicity of dust acoustic solitary waves in dusty plasmas, Zhang et al [32] derived the modifed Zakharov-Kuznetsov (mZK) equation and obtained some exact solutions of the time-fractional mZK equation.…”

Section: Introductionmentioning

confidence: 99%

Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry

Zhang

2021

Complexity

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To construct fractional rogue waves, this paper first introduces a conformable fractional partial derivative. Based on the conformable fractional partial derivative and its properties, a fractional Schrödinger (NLS) equation with Lax integrability is then derived and first- and second-order fractional rogue wave solutions of which are finally obtained. The obtained fractional rogue wave solutions possess translational coordination, providing, to some extent, the degree of freedom to adjust the position of the rogue waves on the coordinate plane. It is shown that the obtained first- and second-order fractional rogue wave solutions are steeper than those of the corresponding NLS equation with integer-order derivatives. Besides, the time the second-order fractional rogue wave solution undergoes from the beginning to the end is also short. As for asymmetric fractional rogue waves with different backgrounds and amplitudes, this paper puts forward a way to construct them by modifying the obtained first- and second-order fractional rogue wave solutions.

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“…The solution of partial differential equation is of great practical significance [19], [20]. Therefore, many different methods are used to calculate the exact and numerical solutions of the equation [21]- [23]. In order to reflect the dissipative effect more intuitively, the Jacobi elliptic function expansion method which can produce periodic solution can be chosen to derive the exact solution [24], [25].…”

Section: Introductionmentioning

confidence: 99%

A Kind of New Coupled Model for Rossby Waves in Two Layers Fluid

et al. 2020

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Waves in nature always interact with each other. In this paper, Rossby waves in two layers fluid with dissipation and exogenous are studied. Form the dimensionless baroclinic quasi-geostrophic vortex equations include exogenous and dissipative, the new (2+1)-dimensional coupled ZK-mZK equations are established. Based on the semi-inverse and Agrawal's method, the time-fractional equations are derived. Then, their conservation laws are analyzed, which may provide bases for the theoretical study. Finally, the exact and numerical solutions of the time-fractional coupled ZK-mZK equations are discussed. By comparison, the alternative variational iteration method gives a high-precision numerical solution of the time-fractional coupled ZK-mZK equations. Further, the solutions show that Rossby waves in two layers fluid change with the change of time, order of fractional derivative and coefficient of coupling term. INDEX TERMS two layers fluid, Rossby waves, time-fractional coupled ZK-mZK equations, alternative variational iteration method

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Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas

Cited by 15 publications

References 44 publications

Modelling and Analysis of Complex Viscous Fluid in Thin Elastic Tubes

Modelling and Analysis of Complex Viscous Fluid in Thin Elastic Tubes

Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry

A Kind of New Coupled Model for Rossby Waves in Two Layers Fluid

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