New optical solitons for complex Ginzburg–Landau equation with beta derivatives via two integration algorithms

Ouahid, Loubna; Abdou, M. A.; Owyed, Saud; Abdel-Baset, A. M.; Yusuf, Abdullahi

doi:10.1007/s12648-021-02168-0

Cited by 7 publications

(3 citation statements)

References 61 publications

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“…The whole of these FNEEs, FNPDEs, FNDDEs remains an ongoing task due to the fact that, the power of memory effect is of great interest in the modeling field's. From the mathematical point of view, the classical systems (integer-order derivatives modeling) are not thoughtfully to address this memory effect issue [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Obviously, different researchers demonstrated that, through the fractional-order derivatives (non-integer operators) it is possible to carry out more on memory effect.…”

Section: Introductionmentioning

confidence: 99%

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

Fendzi-Donfack,

Fotoula,

Jantschi

et al. 2024

Preprint

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This work aims to delve exact physical wave solutions of nonlinear diﬀerential-diﬀerence equations with beta-derivative leading the conduction of nerve impulse dynamics in coupled nerve ﬁbers. The technique performed here names the polynomial expansion method. By employing a new variable through a fractional complex transformation, we turn the electrical model equation to a second-order elliptic nonlinear ordinary diﬀerential equation with two free parameters including the semi-discrete approximation. We extract short pulse, kink, anti-kink, singular kink/anti-kink and kink-rogue solitary waves as solutions of the derived elliptic nonlinear ordinary diﬀerential equations. By carrying out these various solutions, we peruse the dynamical behavior of the current nerve ﬁbers model by investigating their linear stability. We also study the dynamics of the model by applying the ﬁxed points theory and derive the related Jacobian matrix. Throughout the convenient physiological parameters values and signs, we display some 3D modulational instability zones. Furthermore, we also exhibit 3D and 2D graphs presenting the shapes of new pursued solitary waves. The numerous solutions families obtained and plotted help us to show the fractional-order parameter eﬀects in addition of the nerve ﬁber diameter on the amplitude and speed of the nerve impulse propagating inside the coupled nerve ﬁbers. The good or bad coordination of the movement inside the human parts can be explain through the amplitude varying, speed modiﬁcation of the nerve impulse ﬂowing into the coupled nerve ﬁbers. Aiming to this, we make the evolved mathematical framework accessible and highlight potential medical and biological applications. In addition, we enhance the understanding of nerve conduction mechanisms in myelinated ﬁbers.

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Section: Introductionmentioning

confidence: 99%

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

Fendzi-Donfack,

Fotoula,

Jantschi

et al. 2024

Preprint

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“…In recent decades, fractional order calculations have attracted many researchers because they are extremely applicable to real-world issues [1][2][3]. There are several mathematical models [4][5][6][7][8][9][10][11][12][13][14] that apply to the last of these sciences in many fields such as engineering physics, plasma physics, fluid dynamics and mathematical chemistry [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

New analytical solutions of fractional (HIV-1 infection of CD4 + T-cells) using two efficient methods

Alshahrani,

Ouahid,

Abdou

et al. 2023

Preprint

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Here, we use a fractional model to perform an analytical investigation of (HIV-1 infection of CD4+ T-cells). This considered model is analyzed by utilizing a new extended sub-equation method as well as a direct algebraic method. The obtained results demonstrate the influence and superiority of the applied schemes over other analytical methodologies. The series of single solutions with a fractional derived in order achieved with these methods can be classified as trigonometric, hyperbolic, rational, and other basic functions. A comparison of analytical method results is discussed. We also offer some figures showing how exact the solutions are obtained using the two new analytical methods.

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“…Akar and Ozkan handled the sub-equation procedure [20]. Ouahid considered the unified solver technique [21]. Islam et al used a modified simple equation method [22].…”

Section: Introductionmentioning

confidence: 99%

Wave Propagation and Stability Analysis for Ostrovsky and Symmetric Regularized Long-Wave Equations

Kaplan,

Alqahtani,

Alharthi

2023

Mathematics

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This work focuses on the propagation of waves on the water’s surface, which can be described via different mathematical models. Here, we apply the generalized exponential rational function method (GERFM) to several nonlinear models of surface wave propagation to identify their multiple solitary wave structures. We provide stability analysis and graphical representations for the considered models. Additionally, this paper compares the results obtained in this work and existing solutions for the considered models in the literature. The effectiveness and potency of the utilized approach are demonstrated, indicating their applicability to a broad range of nonlinear partial differential equations in physical phenomena.

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New optical solitons for complex Ginzburg–Landau equation with beta derivatives via two integration algorithms

Cited by 7 publications

References 61 publications

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

New analytical solutions of fractional (HIV-1 infection of CD4 + T-cells) using two efficient methods

Wave Propagation and Stability Analysis for Ostrovsky and Symmetric Regularized Long-Wave Equations

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