Time-fractional electron-acoustic shocks in magnetoplasma with superthermal electrons

Khan, Khalid Ali; Ali, Amir; Irfan, M.; Algahtani, Obaid

doi:10.1016/j.aej.2022.09.046

Cited by 4 publications

(3 citation statements)

References 37 publications

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“…The effects of the different parameters were shown to verify the results obtained in this manuscript. The numerical illustration of the BVPs investigated that the existence and uniqueness results with Ulam stability comprise one of the challenging tasks to investigate for such problems [32][33][34][35][36][37]. The physical systems in the fields of plasma physics, electrical engineering, and biological models, hybrid fractional sequential integro-differential equations (HFSID) play a key role due to their double-fractional-order derivative.…”

Section: Discussionmentioning

confidence: 99%

Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory

Algahtani

2022

Symmetry

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In this paper, a variety of boundary value problems (BVPs) known as hybrid fractional sequential integro-differential equations (HFSIDs) with two point orders (p,q) are investigated. The uniqueness and existence of the solution are discussed via Banach fixed-point theorems. Certain particular theorems associated with Hyers–Ulam and Hyers–Ulam–Rassias stability to the solution, as well as the uniqueness and existence of the solution of the BVPs are studied. The results are illustrated with some particular examples, and the numerical data are analyzed for confirmation of the results. The results obtained in this work are simple and can easily be applicable to physical systems. Furthermore, symmetry analysis of fractional differential equations and HFSIDs are also presented. This is due to the fact that the aforementioned analysis plays a significant role in both the optimization and qualitative theory of fractional differential equations.

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Section: Discussionmentioning

confidence: 99%

Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory

Algahtani

2022

Symmetry

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“…In recent decades, due to the broad applications of soliton theory in physics, mathematics, and other areas of engineering and applied sciences, the analysis of explicit accurate solutions in the form of solitary wave solutions of evolution equations has played a significant role [1][2][3]. In soliton theory, several analytical methods can be applied to calculate the approximate solution to nonlinear partial differential equations [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Investigation of a Spatio-Temporal Fractal Fractional Coupled Hirota System

Algahtani

2024

Fractal Fract

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This article aims to examine the nonlinear excitations in a coupled Hirota system described by the fractal fractional order derivative. By using the Laplace transform with Adomian decomposition (LADM), the numerical solution for the considered system is derived. It has been shown that the suggested technique offers a systematic and effective method to solve complex nonlinear systems. Employing the Banach contraction theorem, it is confirmed that the LADM leads to a convergent solution. The numerical analysis of the solutions demonstrates the confinement of the carrier wave and the presence of confined wave packets. The dispersion nonlinear parameter reduction equally influences the wave amplitude and spatial width. The localized internal oscillations in the solitary waves decreased the wave collapsing effect at comparatively small dispersion. Furthermore, it is also shown that the amplitude of the solitary wave solution increases by reducing the fractal derivative. It is evident that decreasing the order α modifies the nature of the solitary wave solutions and marginally decreases the amplitude. The numerical and approximation solutions correspond effectively for specific values of time (t). However, when the fractal or fractional derivative is set to one by increasing time, the wave amplitude increases. The absolute error analysis between the obtained series solutions and the accurate solutions are also presented.

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“…The most practical approach to studying nonlinear PDEs is to employ a reduction perturbation method. This method gives the linear approximation at the first order, which is often the slowly varying envelope approximation of the considered system, described as weakly nonlinear [16][17][18]. On the other hand, the Lie group method is an effective method for studying conservation laws, performing Lie symmetry analysis, and finding exact solutions to nonlinear partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Higher Order Non-Planar Electrostatic Solitary Potential in a Streaming Electron-Ion Magnetoplasma: Phase Plane Analysis

et al. 2023

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We investigate cylindrical and spherical solitons in electron-ion (EI) plasma that contains hot (cold) electrons with stationary ions. The magneto-hydrodynamic equations are solved with the aid of the reductive perturbation (RP) technique, leading to the modified Korteweg–De Vries (mKdV) equation for the non-linear behaviour of the solitary waves in EI plasma. By employing the reduced differential transform method (RDTM), an approximate solution of the mKdV is obtained for solitary waves. Phase plane analysis reveals that these excitations exhibit periodic oscillations. The phase plane and periodic behaviour of the obtained model are studied. It is observed that the amplitude and width of the electron acoustic waves (EAWs) are affected by a slight change in the cold to hot electron temperature ratio (σc) and the number density of the cold to hot electron ratio (α). The effect of the streaming speed u(0) and superthermality index κe are investigated. This study is important for understanding the symmetric properties of cylindrical and spherical plasma, relying on the bifurcation analysis, impacted by the streaming effect in the EI plasma.

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Time-fractional electron-acoustic shocks in magnetoplasma with superthermal electrons

Cited by 4 publications

References 37 publications

Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory

Ulam Stability of Fractional Hybrid Sequential Integro-Differential Equations with Existence and Uniqueness Theory

Investigation of a Spatio-Temporal Fractal Fractional Coupled Hirota System

Higher Order Non-Planar Electrostatic Solitary Potential in a Streaming Electron-Ion Magnetoplasma: Phase Plane Analysis

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