Exact solitary wave solutions of fractional modified Camassa-Holm equation using an efficient method

Zulfiqar, Aniqa; Ahmad, Jamshad

doi:10.1016/j.aej.2020.06.002

Cited by 46 publications

(6 citation statements)

References 43 publications

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“…Different types of exact solitons of our concerned model have been achieved with the use of different methods. Likely, some distinct kind of travelling wave solitons of SMCHM have been attained with the help of generalized (G ′ /G)-expansion scheme in [15], solitary wave solitons are gained through Exp-function technique in [16], different types of wave solutions have been gained by utilizing the Riccati-Bernoulli sub-ODE scheme in [17] etc.…”

Section: Of 23mentioning

confidence: 99%

New Types Of M-fractional Wave Solitons To The Mathematical Physics Model By Three Distinct Techniques

Zafar,

Abukhaled,

Raheel

et al. 2023

Preprint

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In this paper, new types of M-fractional wave solutions of mathematical physics model named as truncated M-fractional (1+1)-dimensional non-linear simplified Modified Camassa-Holm model are achieved by applying the modified simplest equation (MSE), Sardar sub-equation and generalized Kudryashov techniques. The gained solutions containing dark, bright, periodic and mixed wave solitons. Effect of fractional order derivative is also discussed. Achieved wave solitons are verified by Mathematica tool. Few of the gained wave solitons are also described through 2-dimensional, 3-dimensional and contour graphs through Mathematica tool. The gained solutions are helpful for the further development of concerned model. Finally, these techniques are simple, fruitful and effective to deal with non-linear FPDEs.

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Section: Of 23mentioning

confidence: 99%

New Types Of M-fractional Wave Solitons To The Mathematical Physics Model By Three Distinct Techniques

Zafar,

Abukhaled,

Raheel

et al. 2023

Preprint

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“…He and Wu were the inventors of the Exp-function method [20] that was effectively extended to FDEs [21]. e Expfunction method has been applied to several nonlinear FDEs [22][23][24][25][26][27][28][29][30][31][32][33][34]. Recently, many authors worked on the new results of the fractional calculus [35].…”

Section: Introductionmentioning

confidence: 99%

Wave Propagations in Nonlinear Low-Pass Electrical Transmission Lines through Optical Fiber Medium

Zulfiqar

Ahmad

Rani

et al. 2022

Mathematical Problems in Engineering

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The present article discovers the new soliton wave solutions and their propagation in nonlinear low-pass electrical transmission lines (NLETLs). Based on an innovative Exp-function method, multitype soliton solutions of nonlinear fractional evolution equations of NLETLs are established. The equation is reformulated to a fractional-order derivative by using the Jumarie operator. Some new results are also presented graphically to understand the real physical importance of the studied model equation. The physical interpretation of waves is represented in the form of three-dimensional and contour graphs to visualize the underlying dynamic behavior of these solutions for particular values of the parameters. Moreover, the attained outcomes are generally new for the considered model equation, and the results show that the used method is efficient, direct, and concise which can be used in more complex phenomena.

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“…Islam et al [19] obtained the solitary wave solution of the simpli ed modi ed Camassa-Holm equation. Zul qar and Ahmad [20] used the Exp-function scheme to investigate the solitary wave solutions of the fractional simplified mCH model. Khatun et al [21] studied the explicit solutions of the mCH equation with fractional order.…”

Section: Introductionmentioning

confidence: 99%

A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

Fang

Nadeem

Wahash

2022

Journal of Mathematics

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This paper presents the approximate solution of the nonlinear acoustic wave propagation model is known as the modified Camassa–Holm (mCH) equation with the Caputo fractional derivative. We examine this study utilizing the Laplace transform ( ℒ T) coupled with the homotopy perturbation method (HPM) to construct the strategy of the Laplace transform homotopy perturbation method ( ℒ T-HPM). Since the Laplace transform is suitable only for a linear differential equation, therefore ℒ T-HPM is the suitable approach to decompose the nonlinear problems. This scheme produces an iterative formula for finding the approximate solution of illustrated problems that leads to a convergent series without any small perturbation and restriction. Graphical results demonstrate that ℒ T-HPM is simple, straightforward, and suitable for other nonlinear problems of fractional order in science and engineering.

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Exact solitary wave solutions of fractional modified Camassa-Holm equation using an efficient method

Cited by 46 publications

References 43 publications

New Types Of M-fractional Wave Solitons To The Mathematical Physics Model By Three Distinct Techniques

New Types Of M-fractional Wave Solitons To The Mathematical Physics Model By Three Distinct Techniques

Wave Propagations in Nonlinear Low-Pass Electrical Transmission Lines through Optical Fiber Medium

A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

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