Solitons and Periodic Solutions of the Fisher Equation with Nonlinear Ordinary Differential Equation as Auxiliary Equation

Khan, Anika Tashin; Naher, Hasibun

doi:10.12691/ajams-6-6-5

Cited by 6 publications

(1 citation statement)

References 25 publications

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“…Finding exact solutions can be a challenging task, so many researchers have developed numerous methods [1][2][3] for it. Some of them are the first integral method [4,5], the new extended G ′ /G-expansion method [6], the tanh method [7], and the hyperbolic B-spline differential quadrature method [8]. The concept of fractionalorder derivatives was first introduced by Leibniz in 1695.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Analysis and Wave Solutions of the Fisher Equation Using Conformal Fractional Derivatives

Saini,

Kumar,

Deeksha

et al. 2023

Journal of Applied Mathematics

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In the present article, the time fractional Fisher equation is considered in conformal form to study the application of the Lie classical method and quantitative analysis. The Lie symmetry method has been applied to find the infinitesimal generators and symmetry reductions of the fractional Fisher equation. The obtained reduced form of the equation is solved by the method of G ′ / G , which gives different forms of solutions. The theory of bifurcation has been utilized in the reduced form to check the stability and nature of critical points by transforming the equations into an autonomous system. Some phase portraits have been drawn at different critical points by the use of maple.

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Section: Introductionmentioning

confidence: 99%

Symmetry Analysis and Wave Solutions of the Fisher Equation Using Conformal Fractional Derivatives

Saini,

Kumar,

Deeksha

et al. 2023

Journal of Applied Mathematics

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Exact solutions to the family of Fisher's reaction‐diffusion equation using Elzaki homotopy transformation perturbation method

Loyinmi

Akinfe

2020

Engineering Reports

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In this research work, we propose an unprecedented hybrid algorithm which involves the coupling of a new integral transform, namely, the Elzaki transform and the well‐known homotopy perturbation method called the Elzaki homotopy transformation perturbation method (EHTPM) to solve for the exact solution of three distinct types of Fisher's equation, namely, the Fisher's equation of two cases, the sixth‐order Fisher's equation and the nonlinear diffusion equation of the Fisher type. These equations are prominent in mathematical biology and highly applicable in genetic propagation, population dynamics, stochastic processes, combustion theory, as well as a prototype model for a spreading flame, and so on. The efficacy and authenticity of this method was established via convergence and error analysis, and shows that the solutions obtained from EHTPM are unique and convergent. The results of EHTPM when compared with the exact results, homotopy results, and results from the other existing literature via table of comparison, 3D plots, and the convergence plots validates that EHTPM is an efficient and reliable tool of providing exact solutions to a wider class of nonlinear partial differential equations in a simple and straightforward manner, with no discretization, linearization, computation of Adomian polynomials, and devoid of errors.

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Analysis of mixed soliton solutions for the nonlinear Fisher and diffusion dynamical equations under explicit approach

Alqahtani,

Iqbal,

Seadawy

et al. 2024

Opt Quant Electron

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Solitons and Periodic Solutions of the Fisher Equation with Nonlinear Ordinary Differential Equation as Auxiliary Equation

Cited by 6 publications

References 25 publications

Symmetry Analysis and Wave Solutions of the Fisher Equation Using Conformal Fractional Derivatives

Symmetry Analysis and Wave Solutions of the Fisher Equation Using Conformal Fractional Derivatives

Exact solutions to the family of Fisher's reaction‐diffusion equation using Elzaki homotopy transformation perturbation method

Analysis of mixed soliton solutions for the nonlinear Fisher and diffusion dynamical equations under explicit approach

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