Impact of Brownian Motion on the Analytical Solutions of the Space-Fractional Stochastic Approximate Long Water Wave Equation

Al‐Askar, Farah M.; Mohammed, Wael W.; Alshammari, Mohammad

doi:10.3390/sym14040740

Cited by 17 publications

(11 citation statements)

References 33 publications

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“…On the other hand, fractional partial differential equations (FPDEs) have been used to explain many physical phenomena in biology, physics, finance, engineering applications, electromagnetic theory, mathematical, signal processing, and different scientific studies; see, for example, [25][26][27][28][29][30][31][32][33][34][35]. These new fractional-order models are better equipped than the previously utilized integer-order models because fractional-order integrals and derivatives allow for the representation of memory and hereditary qualities of different substances [36].…”

Section: Introductionmentioning

confidence: 99%

The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method

Al‐Askar

Mohammed

2022

Advances in Mathematical Physics

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This article considers the stochastic fractional Radhakrishnan-Kundu-Lakshmanan equation (SFRKLE), which is a higher order nonlinear Schrödinger equation with cubic nonlinear terms in Kerr law. To find novel elliptic, trigonometric, rational, and stochastic fractional solutions, the Jacobi elliptic function technique is applied. Due to the Radhakrishnan-Kundu-Lakshmanan equation’s importance in modeling the propagation of solitons along an optical fiber, the derived solutions are vital for characterizing a number of key physical processes. Additionally, to show the impact of multiplicative noise on these solutions, we employ MATLAB tools to present some of the collected solutions in 2D and 3D graphs. Finally, we demonstrate that multiplicative noise stabilizes the analytical solutions of SFRKLE at zero.

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Section: Introductionmentioning

confidence: 99%

The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method

Al‐Askar

Mohammed

2022

Advances in Mathematical Physics

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“…Solving the system of algebraic equations in (41) with the help of software MATHEMATICA, we obtain the following solutions:…”

Section: Mathematical Analyses Of the Models And Its Solutionsmentioning

confidence: 99%

“…Recently, many powerful methods for obtaining exact solutions of nonlinear partial differential equations (NLPDEs) have been presented, such as exponential rational function method [21], exp a function, and the hyperbolic function methods [22]. ðG ′ /GÞexpansion method [23,24], ðG′/G, 1/GÞ-expansion method [25,26], Sardar-subequation method [27], new subequation method [28], Riccati equation method [29], homotopy perturbation method [30], extended direct algebraic method [31], Kudryashov method [32], Exp-function method [33], the modified extended exp-function method [34], F-expansion method [35], the Backlund transformation method [36], the extended tanh-method [37], Jacobi elliptic function expansion methods [38], extended sinh-Gordon equation expansion method [39], and different other methods [40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics

Siddique

Mirza

Shahzadi

et al. 2022

Journal of Function Spaces

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In this paper, we obtain the novel exact traveling wave solutions in the form of trigonometric, hyperbolic and exponential functions for the nonlinear time fractional generalized reaction Duffing model and density dependent fractional diffusion-reaction equation in the sense of beta-derivative by using three fertile methods, namely, Generalized tanh (GT) method, Generalized Bernoulli (GB) sub-ODE method, and Riccati-Bernoulli (RB) sub-ODE method. The derived solutions to the aforementioned equations are validated through symbolic soft computations. To promote the vital propagated features; some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the specific values to the parameters under the confine conditions. The accomplished solutions show that the presented methods are not only powerful mathematical tools for generating more solutions of nonlinear time fractional partial differential equations but also can be applied to nonlinear space-time fractional partial differential equations.

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“…How to obtain the exact solution of the NPDEs has always been the purpose of researchers. To this day, some effective methods have been proposed to seek for the exact solution of the NPDEs such as the Bäcklund transformation method [7][8][9][10], Cole-Hopf transformation method [11][12][13][14], variational method [15,16], extended rational sinecosine and sinh-cosh methods [17,18], Sardar subequation method [19,20], the Kudryashov approach [21,22], extended sinh-Gordon equation expansion method [23,24], trial equation method [25,26], sub-equation method [27][28][29], Wang's direct mapping method [30], and so on [31][32][33][34][35]. In this work, we aim to study the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation that reads as [36]:…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Behaviors of the (3+1)-Dimensional B-Type Kadomtsev—Petviashvili Equation in Fluid Mechanics

Wang

Liu

et al. 2023

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This paper provides an investigation on nonlinear dynamic behaviors of the (3+1)-dimensional B-type Kadomtsev—Petviashvili equation, which is used to model the propagation of weakly dispersive waves in a fluid. With the help of the Cole—Hopf transform, the Hirota bilinear equation is established, then the symbolic computation with the ansatz function schemes is employed to search for the diverse exact solutions. Some new results such as the multi-wave complexiton, multi-wave, and periodic lump solutions are found. Furthermore, the abundant traveling wave solutions such as the dark wave, bright-dark wave, and singular periodic wave solutions are also constructed by applying the sub-equation method. Finally, the nonlinear dynamic behaviors of the solutions are presented through the 3-D plots, 2-D contours, and 2-D curves and their corresponding physical characteristics are also elaborated. To our knowledge, the obtained solutions in this work are all new, which are not reported elsewhere. The methods applied in this study can be used to investigate the other PDEs arising in physics.

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Impact of Brownian Motion on the Analytical Solutions of the Space-Fractional Stochastic Approximate Long Water Wave Equation

Cited by 17 publications

References 33 publications

The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method

The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method

Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics

Nonlinear Dynamic Behaviors of the (3+1)-Dimensional B-Type Kadomtsev—Petviashvili Equation in Fluid Mechanics

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