New analytical wave solutions to the M-fractional Kuralay-II equations based on three distinct schemes

Raheel, M.; Zafar, Asim; Ali, Mohamed R.; Myrzakulova, Zhaidary; Bekir, Ahmet; Myrzakulov, Ratbay

doi:10.21203/rs.3.rs-2655711/v1

Cited by 4 publications

(1 citation statement)

References 26 publications

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“…Definition. Consider a function g: (0, ∞ ) → R with order σ, then the truncated M-fractional derivative [34,38] can be written as:…”

Section: M-fractional Truncated Derivativementioning

confidence: 99%

Soliton solutions and sensitive analysis to nonlinear wave model arising in optics

Lu,

Ahmad,

Akram

et al. 2024

Phys. Scr.

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In this study, we use analytical algorithms, specifically the auxiliary equation (AE) approach, the improved $F$-expansion method, and modified Sardar sub equation (MSSE) method to investigate complex wave structures for plentiful solutions associated with the fractional perturbed Gerdjikov-Ivanov (PGI) model with the $M$-fractional operator. The investigated model is a well-established mathematical model used to represent a variety of physical events in nonlinear dynamics and mathematical physics. By using the aforementioned techniques, we scrutinize some new optical wave solutions in the forms of dark, bright, periodic, combo, $W$-shaped, $M$-shape, $V$-shape, kink type, singular rational, exponential, trigonometric, and hyperbolic solutions. The acquired solutions address a wide range of optical solutions in the form of 3D-plots, contour plots, and 2D plots, declaring the free parameters of such optical soliton solutions and comprehending their dynamic behaviour. Also, the sensitive analysis of selected model is analyzed. \textcolor{green}{The main contribution of this study is to extract diverse solitary wave solutions of the adopted model. Some of the solutions are similar and some diverge from the previous solutions which justify the novelty of the study.} Finally, we discovered that the current technique provides a reliable instrument for investigating the analytic solutions of fractional differential equations. The proposed PGI model can be used to transmit ultra-fast pulses across optical fibers. This research goes beyond to the advancement of mathematical techniques for solving fractional differential equations and broadens their application to a wide range of real-world scientific and engineering problems.

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“…Definition. Consider a function g: (0, ∞ ) → R with order σ, then the truncated M-fractional derivative [34,38] can be written as:…”

Section: M-fractional Truncated Derivativementioning

confidence: 99%

Soliton solutions and sensitive analysis to nonlinear wave model arising in optics

Lu,

Ahmad,

Akram

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

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Stability analysis and solitonic behaviour of Schrödinger’s nonlinear (2+1) complex conformable time fractional model

Ahmad,

Noor,

Akram

2024

Opt Quant Electron

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Explorating the solition solutions of fractional Chen–Lee–Liu equation with birefringent fibers arising in optics and their sensitive analysis

ur Rahman,

AL-Essa

2024

Opt Quant Electron

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New analytical wave solutions to the M-fractional Kuralay-II equations based on three distinct schemes

Cited by 4 publications

References 26 publications

Soliton solutions and sensitive analysis to nonlinear wave model arising in optics

Soliton solutions and sensitive analysis to nonlinear wave model arising in optics

Stability analysis and solitonic behaviour of Schrödinger’s nonlinear (2+1) complex conformable time fractional model

Explorating the solition solutions of fractional Chen–Lee–Liu equation with birefringent fibers arising in optics and their sensitive analysis

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