Investigation of Fractional Order Sine-Gordon Equation Using Laplace Adomian Decomposition Method

Ali, Amir; Gul, Zamin; Khan, Wajahat Ali; Ahmad, Saeed; Zeb, Salman

doi:10.1142/s0218348x21501218

Cited by 30 publications

(13 citation statements)

References 40 publications

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“…This method is used here for the first to study the nonlinear evolution of solitary potential in nonextensive plasma. The modified double Laplace decomposition method has also extensively used to reduce the spatiotemporal solutions corresponds for the linear as well as nonlinear deferential equation [40][41][42][43][44] .…”

Section: Modified Double Laplace Decomposition Methods (Mdldm)mentioning

confidence: 99%

Electron-acoustic solitary potential in nonextensive streaming plasma

Khan

Algahtani

Irfan

et al. 2022

Sci Rep

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The linear/nonlinear propagation characteristics of electron-acoustic (EA) solitons are examined in an electron-ion (EI) plasma that contains negative superthermal (dynamical) electrons as well as positively charged ions. By employing the magnetic hydrodynamic (MHD) equations and with the aid of the reductive perturbation technique, a Korteweg-de-Vries (KdV) equation is deduced. The latter admits soliton solution suffering from the superthermal electrons and the streaming flow. The utility of the modified double Laplace decomposition method (MDLDM) leads to approximate wave solutions associated with higher-order perturbation. By imposing finite perturbation on the stationary solution, and with the aid of MDLDM, we have deduced series solution for the electron-acoustic excitations. The latter admits instability and subsequent deformation of the wave profile and can’t be noticed in the KdV theory. Numerical analysis reveals that thermal correction due to superthermal electrons reduces the dimensionless phase speed $$(\bar{U}_{ph})$$ ( U ¯ ph ) for EA wave. Moreover, a random motion spread out the dynamical electron fluid and therefore, gives rise to $$\bar{U}_{ph}$$ U ¯ ph . A degree enhancement in temperature of superthermal (dynamical) electrons tappers of (increase) the wave steeping and the wave dispersion, enhancing (reducing) the pulse amplitude and the spatial extension of the EA solitons. Interestingly, the approximate wave solution suffers oscillation that grows in time. Our results are important for understanding the coherent EA excitation, associated with the streaming effect of electrons in the EI plasma being relevant to the earth’s magnetosphere, the ionosphere, the laboratory facilities, etc.

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Section: Modified Double Laplace Decomposition Methods (Mdldm)mentioning

confidence: 99%

Electron-acoustic solitary potential in nonextensive streaming plasma

Khan

Algahtani

Irfan

et al. 2022

Sci Rep

Self Cite

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“…Double Laplace decomposition method has been presented to solve Hirota, Schrödinger and modified KdV equations [48]. Laplace decomposition method has been applied to solve the non-linear fractional Sine-Gordon equations [49]. Benjamin-Bona-Mahony equation has been solved analytically using Laplace Adomian decomposition method [50].…”

Section: 6: Laplace Adomian Decomposition Methodsmentioning

confidence: 99%

A Comprehensive Review on Several Techniques for Solving 2D and 3D Partial Differential Equations

Singh¹,

Singh²

2022

Int. J. Res. Publ. Rev.

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Many Physical phenomenon in Sciences and engineering are modeled in the form of Partial differential equations. Partial differential equations arise in formulation of many mathematical problems may be of one dimensional, two dimensional, three dimensional etc. In this paper, various types of Partial differential equations and methods available in literature for solving two dimensional and three dimensional Partial differential equations are discussed.

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“…New research on the fractional-order mathematical representations under the CPC operator of some other viral diseases can be found in [23][24][25][26]. The Laplace-Adomian decomposition methodology solves stochastic and deterministic differential equations more effectively than traditional techniques by converting differential equations into their algebraic equivalents and decomposing nonlinear elements into Adomain polynomials [27,28].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Transmission and Mathematical Analysis of Ebola Virus Using a Constant Proportional Operator with a Power Law Kernel

Xu,

Farman

2023

Fractal Fract

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The Ebola virus continues to be the world’s biggest cause of mortality, especially in developing countries, despite the availability of safe and effective immunization. In this paper, we construct a fractional-order Ebola virus model to check the dynamical transmission of the disease as it is impacted by immunization, learning, prompt identification, sanitation regulations, isolation, and mobility limitations with a constant proportional Caputo (CPC) operator. The existence and uniqueness of the proposed model’s solutions are discussed using the results of fixed-point theory. The stability results for the fractional model are presented using Ulam–Hyers stability principles. This paper assesses the hybrid fractional operator by applying methods to invert proportional Caputo operators, calculate CPC eigenfunctions, and simulate fractional differential equations computationally. The Laplace–Adomian decomposition method is used to simulate a set of fractional differential equations. A sustainable and unique approach is applied to build numerical and analytic solutions to the model that closely satisfy the theoretical approach to the problem. The tools in this model appear to be fairly powerful, capable of generating the theoretical conditions predicted by the Ebola virus model. The analysis-based research given here will aid future analysis and the development of a control strategy to counteract the impact of the Ebola virus in a community.

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Investigation of Fractional Order Sine-Gordon Equation Using Laplace Adomian Decomposition Method

Cited by 30 publications

References 40 publications

Electron-acoustic solitary potential in nonextensive streaming plasma

Electron-acoustic solitary potential in nonextensive streaming plasma

A Comprehensive Review on Several Techniques for Solving 2D and 3D Partial Differential Equations

Dynamical Transmission and Mathematical Analysis of Ebola Virus Using a Constant Proportional Operator with a Power Law Kernel

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