Nonlinear dynamical wave structures to the Zoomeron equation for population models

2022 ◽  
Author(s):  
Ahmet Bekir ◽  
Emad H. M. Zahran
Keyword(s):  
Exact Solutions ◽  
Fractional Order ◽  
Population Models ◽  
Nonlinear Dynamical ◽  
Wave Solutions ◽  
Biological Population ◽  
First Time

Abstract In this paper, the nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achevied for the first time in the framwork of the Paul-Painlevé approachmethod (PPAM). When the variables appearing in the exact solutions take specific values, the solaitry wave solutions will be easily satisfied.The realized results prove the efficiency of this technique.

scholarly journals New Exact Solutions for High Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongan Xie ◽  
Shengqiang Tang
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Bifurcation Theory ◽  
Solitary Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Light Pulses ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
First Time ◽  
Quintic Nonlinear Schrödinger Equation

We study a class of high dispersive cubic-quintic nonlinear Schrödinger equations, which describes the propagation of femtosecond light pulses in a medium that exhibits a parabolic nonlinearity law. Applying bifurcation theory of dynamical systems and the Fan sub-equations method, more types of exact solutions, particularly solitary wave solutions, are obtained for the first time.

Mathematical study of fractional-order biological population model using optimal homotopy asymptotic method

2016 ◽  
Vol 09 (06) ◽  
pp. 1650081 ◽  
Author(s):  
S. Sarwar ◽  
M. A. Zahid ◽  
S. Iqbal
Keyword(s):  
Fractional Order ◽  
Asymptotic Method ◽  
Population Model ◽  
Approximate Solutions ◽  
High Accuracy ◽  
Population Models ◽  
Mathematical Study ◽  
Third Order ◽  
Biological Population ◽  
Optimal Homotopy Asymptotic Method

In this paper, we study the fractional-order biological population models (FBPMs) with Malthusian, Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method (OHAM) for partial differential equations (PDEs) is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional-order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.

scholarly journals Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Majid Bagheri ◽  
Ali Khani
Keyword(s):  
Fractional Derivative ◽  
Exact Solutions ◽  
Fractional Order ◽  
Kdv Equation ◽  
Time Derivative ◽  
Hyperbolic Function ◽  
Nonlinear Phenomena ◽  
Generalized Kdv Equation ◽  
Wave Solutions ◽  
Fractional Time Derivative

The present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order α . Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional derivative which is used to get many solitary wave solutions by changing various parameters. The obtained solutions include three classes of soliton wave solutions in terms of hyperbolic function, trigonometric function, and rational function solutions. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of nonlinearity. Some of the nonlinear equations arise in fluid dynamics and nonlinear phenomena.

New exact traveling wave solutions of biological population model via the extended rational sinh-cosh method and the modified Khater method

2019 ◽  
Vol 33 (28) ◽  
pp. 1950338 ◽  
Author(s):  
Hadi Rezazadeh ◽  
Alper Korkmaz ◽  
Mostafa M. A. Khater ◽  
Mostafa Eslami ◽  
Dianchen Lu ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Population Model ◽  
Stability Property ◽  
Traveling Wave Solutions ◽  
Algebraic Methods ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Biological Population ◽  
The Stability

In this paper, the extended rational sinh-cosh method (ERSCM) and modified Khater method are applied to the biological population model to derive new exact solutions. Moreover, the stability property of some obtained solutions is discussed to show the ability of them for using in the model’s applications. Implementation of the direct algebraic methods, the equations derived by substitution of the predicted solution are solved. It is significant to point out that new traveling wave solutions are found. The present methods are easy to employ and sufficient to determine the solutions.

On biological population model of fractional order

2016 ◽  
Vol 09 (05) ◽  
pp. 1650070 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Ayyaz Ali ◽  
Bandar Bin-Mohsin
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Fractional Order ◽  
Population Model ◽  
Numerical Data ◽  
Population Changes ◽  
Partial Differential ◽  
Biological Population ◽  
Fractional Pdes

In this paper, we extensively studied a mathematical model of biology. It helps us to understand the dynamical procedure of population changes in biological population model and provides valuable predictions. In this model, we establish a variety of exact solutions. To study the exact solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into corresponding partial differential equation and modified exp-function method is implemented to investigate the nonlinear equation. Graphical demonstrations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, unfailing, well-organized and pragmatic for fractional PDEs and could be protracted to further physical happenings.

Exact Solutions of Fractional-Order Biological Population Model

2009 ◽  
Vol 52 (6) ◽  
pp. 992-996 ◽  
Author(s):  
A. M. A El-Sayed ◽  
S. Z Rida ◽  
A. A. M Arafa
Keyword(s):  
Exact Solutions ◽  
Fractional Order ◽  
Population Model ◽  
Biological Population

Exact propagation of the isolated waves model described by the three coupled nonlinear Maccari’s system with complex structure

2021 ◽  
pp. 2150193
Author(s):  
Emad H. M. Zahran ◽  
Maha S. M. Shehata ◽  
S. M. Mirhosseini-Alizamini ◽  
Md Nur Alam ◽  
Lanre Akinyemi
Keyword(s):  
Exact Solutions ◽  
Complex Structure ◽  
Physical Parameters ◽  
Finite Region ◽  
Wave Solutions ◽  
Accurate Interpretation ◽  
Ode Method ◽  
First Time ◽  
Accurate Wave

In this paper, the three nonlinear Maccari’s-system (TNLMS) which describes how isolated waves are propagated in a finite region of space is studied. New accurate wave solutions of this model are obtained for the first time using the Riccati–Bernoulli Sub-ODE method (RBSOM) that treats the problem for which the balance rule fails. The efficiency of this method for constructing these exact solutions has been demonstrated. The obtained results give an accurate interpretation of the propagation of these isolated waves. With an appropriate values for the physical parameters, some representative wave structures are graphically presented.

scholarly journals New fractional calculus and application to the fractional-order of extended biological population model

2018 ◽  
Vol 36 (3) ◽  
pp. 115-128 ◽  
Author(s):  
Ahmad Neirameh
Keyword(s):  
Solitary Wave ◽  
Fractional Order ◽  
Population Model ◽  
Conformable Fractional Derivative ◽  
Solitary Wave Solutions ◽  
Fractional Partial Differential Equations ◽  
Wave Solutions ◽  
Biological Population ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

In this study, we propose a new algorithm to find exact solitary wave solutions of nonlinear time- fractional order of extended biological population model. The new algorithm basically illustrates how two powerful algorithms, conformable fractional derivative and the homogeneous balance method can be combined and used to get exact solutions of fractional partial differential equations.

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