Multiplicity for fractional differential equations with p-Laplacian

Tian, Yazhou; Wei, Yongfang; Sun, Sujing

doi:10.1186/s13661-018-1049-0

Cited by 22 publications

(10 citation statements)

References 40 publications

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“…So far, the development of fractional derivatives has been very mature, and fractional calculus and the corresponding fractional partial differential equations have attracted wide attention in many subjects [22][23][24][25][26][27][28]. Compared with integer order models, fractional models can better explain nonlinear physical processes and propagation characteristics in real environment [29][30][31][32][33]. However, fractional models were rarely used to study the dust plasma in the past.…”

Section: Introductionmentioning

confidence: 99%

An Application of (3+1)‐Dimensional Time‐Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves

Yang

2019

Complexity

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Dust plasma is a new field of physics which has developed rapidly in recent decades. The study of dust plasma has received much attention due to its importance in the environment of space and the Earth. Dust acoustic waves are generated because of the inertia of dust mass while the restoring force is provided by the thermal pressure of electrons and ions. Since dust acoustic waves were first reported theoretically in unmagnetized dust plasma by Rao et al., they have become a research hot spot. In this paper, the excitation of dust acoustic waves by a gravity field in a dust plasma is analyzed. According to the control equations of dust plasma motion and employing multiscale analysis and perturbation method, we have obtained a (3+1)-dimensional ZK model. Because of the space property of dust plasma, (3+1)-dimensional ZK equation is more suitable than KdV equation and (2+1)-dimensional ZK equation to describe the real dust acoustic waves. Then, the (3+1)-dimensional time-space fractional ZK (TSF-ZK) equation describing the fractal process of nonlinear dust acoustic waves is given for the first time. To further explore how dust acoustic waves change energy as they travel, we discuss the conservation laws of the new model. Moreover, we study the exact solution of (3+1)-dimensional TSF-ZK equation by using extended Kudryashov method. Finally, based on the exact solution, we further investigate the effect of the parameter k, the charge properties of dust particle Zd0, the fractional order values α, β, γ, and θ, the temperature Td, the gravity g, and the collision frequency β0 and β1 on the properties of dust acoustic waves by a gravity field in dust plasma.

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Section: Introductionmentioning

confidence: 99%

An Application of (3+1)‐Dimensional Time‐Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves

Yang

2019

Complexity

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“…In recent years, there has been much attention focused on questions of solutions of twopoint, three-point, multi-point, and integral boundary value problems for nonlinear ordinary differential equations and fractional differential equations. For example, two-point boundary value problems [3,15,29,39], beam equation problems [5,13,16,36], boundary value problems at resonance [2,6,42,43], fractional boundary value problems [8,24], impulsive problems [4,38], multi-point boundary value problems [10,14,20,25,26,32,33,43], integral boundary value problems [7,9,17,21,22,28,37], p-Laplace problems [11,13,24,27,30,31], delay problems [23,34,35], solitons [12], singular problems [3], Schrödinger problem [40,41], etc.…”

Section: Introductionmentioning

confidence: 99%

On positive solutions for some second-order three-point boundary value problems with convection term

2019

Self Cite

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In this paper, a fixed point theorem in a cone and some inequalities of the associated Green's function are applied to obtain the existence of positive solutions of second-order three-point boundary value problem with dependence on the first-order derivative x (t) + f (t, x(t), x (t)) = 0, 0 < t < 1, x(0) = 0, x(1) = μx(η), where f : [0, 1] × [0, ∞) × R → [0, ∞) is a continuous function, μ > 0, η ∈ (0, 1), μη < 1. The interesting point is that the nonlinear term is dependent on the convection term.

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“…Also there has been shown much interest in obtaining the existence and multiplicity of solutions of this class of problems by employing different fixed point theorems. Recently, many scholars have paid more attention to the fractional order differential equation boundary value problems with p-Laplacian operator; see [25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Solvability for a class of nonlinear Hadamard fractional differential equations with parameters

Alesemi

2019

Bound Value Probl

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Multiplicity for fractional differential equations with p-Laplacian

Cited by 22 publications

References 40 publications

An Application of (3+1)‐Dimensional Time‐Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves

An Application of (3+1)‐Dimensional Time‐Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves

On positive solutions for some second-order three-point boundary value problems with convection term

Solvability for a class of nonlinear Hadamard fractional differential equations with parameters

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