Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line

Aslan, İsmail

doi:10.1088/0253-6102/66/3/315

Cited by 36 publications

(12 citation statements)

References 44 publications

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“…In preceding years, enormous research works have been done on NLETLs. Many researchers have been obtaining numerous kind of analytic solution with the help of different methods like Jacobi elliptic method, auxiliary equation method, tanh function method, Ricatti equation technique, Kudryashov technique and modified version of Kudryashov technique, the sine-Gorden method, and the extended form of sine-Gorden equation [39][40][41][42].…”

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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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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“…Finding exact/approximate analytical solutions of FNDDEs has become a vital task. Researchers focused on the FNDDEs and presented some effective methods including the (G′/G)‐expansion method 9,18 and Riccati equation method 19 . Recently, Fang et al extended the Jacobian elliptic function approach 20 and exp‐function method 21 to obtain Jacobian elliptic function and exp‐function solutions of FDDEs.…”

Section: Introductionmentioning

confidence: 99%

“…19 Recently, Fang et al extended the Jacobian elliptic function approach 20 and exp-function method 21 to obtain Jacobian elliptic function and exp-function solutions of FDDEs. These methods in previous studies 9,18,19 simplified FNDDEs into NDDEs with the integer order via a fractional complex transformation. However, some researchers have mentioned that these fractional complex transformations exist an error because Jumarie's basic formulae used in previous studies 9,18,19 need to improve.…”

Section: Introductionmentioning

confidence: 99%

Discrete soliton solutions of the fractional discrete coupled nonlinear Schrödinger equations: Three analytical approaches

Wang

Dai

2021

Math Methods in App Sciences

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The fractional discrete coupled nonlinear Schrödinger equations are solved on account of the modified Riemann–Liouville fractional derivative and Mittag–Leffler function. By using the fractional generalized Riccati method, generalized Mittag–Leffler function method and fractional generalized tanh–sech function method, some new analytical discrete solutions constructed by generalized trigonometric and hyperbolic functions are obtained, including discrete fractional bright soliton, dark soliton, combined soliton, and periodic solutions. In order to illustrate the effect of fractional order parameter on dynamics of fractional discrete soliton, some results in this study are illustrated graphically. Results indicate that although the combined wave is made up of singular coth function, it does not exhibit the singular property in the discrete case. Moreover, two kinds of scalar soliton solutions are found. These results could be of great significance to further study complex nonlinear discrete physical phenomena.

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“…In many research fields, more and more attention has been paid to fractional-order models [60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76]. Recently, Aslan [77][78][79][80] has successfully extended analytical methods-combined symbolic computation to solve fractional semidiscrete equations. How to extend the method used in this paper to such fractional semidiscrete equations is also worthy of studying.…”

Section: Introductionmentioning

confidence: 99%

Analytical Insights into a Generalized Semidiscrete System with Time-Varying Coefficients: Derivation, Exact Solutions, and Nonlinear Soliton Dynamics

Zhang

Zhao

2020

Complexity

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In this paper, a new generalized semidiscrete integrable system with time-varying coefficients is analytically studied. Firstly, the generalized semidiscrete system is derived from a semidiscrete matrix spectral problem by embedding finite time-varying coefficient functions. Secondly, exact and explicit N-soliton solutions of the semidiscrete system are obtained by using the inverse scattering analysis. Finally, three special cases when N=1,2,3 of the obtained N-soliton solutions are simulated by selecting some appropriate coefficient functions. It is shown that the time-varying coefficient functions affect the spatiotemporal structures and the propagation velocities of the obtained semidiscrete one-soliton solutions, two-soliton solutions, and three-soliton solutions.

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Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line

Abstract: Abstract

Cited by 36 publications

References 44 publications

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

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

Discrete soliton solutions of the fractional discrete coupled nonlinear Schrödinger equations: Three analytical approaches

Analytical Insights into a Generalized Semidiscrete System with Time-Varying Coefficients: Derivation, Exact Solutions, and Nonlinear Soliton Dynamics

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