Adequate soliton solutions to the space–time fractional telegraph equation and modified third-order KdV equation through a reliable technique

Arefin, Mohammad Asif; Sadiya, Umme; İnç, Mustafa; Uddin, M. Hafiz

doi:10.1007/s11082-022-03640-9

Cited by 30 publications

(3 citation statements)

References 44 publications

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“…Te versatility of fractional calculus is evident in its applications across diverse felds such as bioengineering, rheology, viscoelasticity, acoustics, optics, robotics, control theory, chemical and statistical physics, and electrical and mechanical engineering [5][6][7][8]. One may even claim that fractional-order systems in general explain real-world occurrences.…”

Section: Introductionmentioning

confidence: 99%

Utilizing the Optimal Auxiliary Function Method for the Approximation of a Nonlinear Long Wave System considering Caputo Fractional Order

Iqbal,

Nawaz,

Hina

et al. 2024

Complexity

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In this article, we explore the utilization of the Caputo derivative and the Riemann–Liouville (R–L) fractional integral to analyze the optimal auxiliary function method for approximating fractional nonlinear long waves. Approximate long wave equation with a distinct dispersion relation offers the most accurate description of shallow water wave properties. Various methods, including the Adomian decomposition technique, the variational iteration method, the optimum homotopy asymptotic method, and the new iterative technique, have been employed and compared to those obtained using the fractional-order approximate long wave equation. The results of our study indicate that the optimal auxiliary function method is highly successful and practically simple, achieving better and more rapid convergence after just one repetition. This method is recognized as an efficient approach, demonstrating high precision in solving intriguing and intricate problems. Furthermore, it proves to be more time and resource efficient than other relevant analytical techniques, leading to significant savings in both volume and time. Compared to the Adomian decomposition technique, the new iterative technique, the variational iteration method, and the optimum homotopy asymptotic method, the suggested technique is extremely accurate computationally. It is also easy to analyze and solve fractionally linked nonlinear complex phenomena that arise in science and technology. We present the numerical and graphical findings that support these conclusions.

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Section: Introductionmentioning

confidence: 99%

Utilizing the Optimal Auxiliary Function Method for the Approximation of a Nonlinear Long Wave System considering Caputo Fractional Order

Iqbal,

Nawaz,

Hina

et al. 2024

Complexity

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“…The mathematical modeling of engineering and physical problems is inherently governed by NLPDEs, which underscores the importance and intrigue of searching for closed-form wave solutions of NLPDEs. Many researchers have studied the analytical wave solutions of NLPDEs, and they've come up with lots of useful methods to solve them, such as the sine-cosine method [1], the modified simple equation technique [2], the Exp-function process [3], the modified Exp-function process [4], the nonlinear transformation method [5], the Khater method [6], He's homotopy perturbation technique [7], the variational method [8], the functional variable method [9], the extended direct algebraic method [10], the Bernoulli sub-equation function method [11], the Adomian decomposition method [12], the exp(−f(ξ)) expansion method [13], the (G G ¢ )-expansion process and its various modifications [14][15][16][17][18][19], the enhanced Kudryashov method [20], the extended tanh-function technique [21], the modified extended tanh-function procedure [22], and others [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Diverse soliton solutions to the nonlinear partial differential equations related to electrical transmission line

Sagib,

Saha,

Mohanty

et al. 2024

Phys. Scr.

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This paper introduces novel traveling wave solutions for the (1+1)-dimensional nonlinear telegraph equation (NLTE) and the (2+1)-dimensional nonlinear electrical transmission line equation (NETLE). These equations are pivotal in the transmission and propagation of electrical signals, with applications in telegraph lines, digital image processing, telecommunications, and network engineering. We applied the improved tanh technique combined with the Riccati equation to derive new solutions, showcasing various solitary wave patterns through 3D surface and 2D contour plots. These results provide more comprehensive solutions than previous studies and offer practical applications in communication systems utilizing solitons for data transmission. The proposed method demonstrates an efficient calculation process, aiding researchers in analyzing nonlinear partial differential equations in applied mathematics, physics, and engineering.

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“…In Ref. [18], multiple soliton solutions ranging from king type, single soliton and double soliton to multiple solitons were offered for space-time fractional modified KdV equations. These methods can also be used to obtain soliton, periodical, and rogue wave solutions for the Ivancevic equation [19][20][21][22], which defines the option-pricing wave function in terms of the stock price and time.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion

Zeng

Liang

et al. 2023

Symmetry

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The exact traveling wave solutions to coupled KdV equations with variable coefficients are obtained via the use of quadratic Jacobi’s elliptic function expansion. The presented coupled KdV equations have a more general form than those studied in the literature. Nine couples of quadratic Jacobi’s elliptic function solutions are found. Each couple of traveling wave solutions is symmetric in mathematical form. In the limit cases m→1, these periodic solutions degenerate as the corresponding soliton solutions. After the simple parameter substitution, the trigonometric function solutions are also obtained.

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Adequate soliton solutions to the space–time fractional telegraph equation and modified third-order KdV equation through a reliable technique

Cited by 30 publications

References 44 publications

Utilizing the Optimal Auxiliary Function Method for the Approximation of a Nonlinear Long Wave System considering Caputo Fractional Order

Utilizing the Optimal Auxiliary Function Method for the Approximation of a Nonlinear Long Wave System considering Caputo Fractional Order

Diverse soliton solutions to the nonlinear partial differential equations related to electrical transmission line

Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion

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