A Decomposition Method for Solving the Fractional Davey-Stewartson Equations

Quantum calculus (also known as the q-calculus) is a technique that is similar to traditional calculus, but focuses on the concept of deriving q-analogous results without the use of the limits. In this paper, we suggest and analyze some new q-iterative methods by using the q-analogue of the Taylor’s series and the coupled system technique. In the domain of q-calculus, we determine the convergence of our proposed q-algorithms. Numerical examples demonstrate that the new q-iterative methods can generate solutions to the nonlinear equations with acceptable accuracy. These newly established methods also exhibit predictability. Furthermore, an analogy is settled between the well known classical methods and our proposed q-Iterative methods.

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“…Theorem 1 (see [34]). If M is a contraction mapping, the defined series in (16) is absolutely convergent.…”

Section: Construction Of the Q-iterative Methodsmentioning

confidence: 99%

“…Many linear and nonlinear models appearing in science and engineering problems can be modeled by using the q differential equations. Jafari et al [34] have adopted Daftardar decomposition technique for solving the q difference equations and also determined the convergence of the method.…”

Section: Introductionmentioning

confidence: 99%

On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus

et al. 2021

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“…Some authors used two different approaches, namely, the Riccati-Bernoulli sub-ordinary differential equations and sine-cosine methods, to obtain novel elliptic, hyperbolic, trigonometric, and rational stochastic solutions [33]. In another study, a new iterative method was proposed to solve fractional DSS [34]. The convergence of this method was proved, and the results obtained were compared with the exact solutions, demonstrating the effectiveness of this approach.…”

Section: Mathematical Modelmentioning

confidence: 99%

Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

Molina-Holguín,

Urenda-Cázares,

Macías-Díaz

et al. 2024

Fractal Fract

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In this article, a generalized form of the Davey–Stewartson system, consisting of three nonlinear coupled partial differential equations, will be studied. The system considers the presence of fractional spatial partial derivatives of the Riesz type, and extensions of the classical mass, energy, and momentum operators will be proposed in the fractional-case scenario. In this work, we will prove rigorously that these functionals are conserved throughout time using some functional properties of the Riesz fractional operators. This study is intended to serve as a stepping stone for further exploration of the generalized Davey–Stewartson system and its wide-ranging applications.

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“…It is worth to pointing out at here that the above type of equation such as Davey-Stewartson (DS) equation has been investigated by different methods like first integral method [17], variational iteration method [18] and decomposition method [19], but gauge transformation approach [20] which is employed to investigate the model equations. ( 2) is more effective and handy to generate multi soliton solution.…”

Section: Bright Solitons and Collisional Dynamicsmentioning

confidence: 99%

Manipulation of light in a generalized coupled Nonlinear Schrödinger equation

Radha¹,

Vinayagam²,

Porsezian

2016

Communications in Nonlinear Science and Numerical Simulation

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We investigate a generalized coupled nonlinear Schrodinger (GCNLS) equation containing Self-Phase Modulation (SPM), Cross-Phase Modulation (XPM) and Four Wave Mixing (FWM) describing the propagation of electromagnetic radiation through an optical fibre and generate the associated Lax-pair. We then construct bright solitons employing gauge transformation approach. The collisional dynamics of bright solitons indicates that it is not only possible to manipulate intensity (energy) between the two modes (optical beams), but also within a given mode unlike the Manakov model which does not have the same freedom. The freedom to manipulate intensity (energy) in a given mode or between two modes arises due to a suitable combination of SPM, XPM and FWM. While SPM and XPM are controlled by an arbitrary real parameter each, FWM is governed by two arbitrary complex parameters. The above model may have wider ramifications in nonlinear optics and Bose-Einstein Condensates (BECs).

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A Decomposition Method for Solving the Fractional Davey-Stewartson Equations

Cited by 7 publications

References 15 publications

On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus

On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus

Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

Manipulation of light in a generalized coupled Nonlinear Schrödinger equation

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