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Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized G/G-expansion method

Onur Alp Ilhan, Haci Mehmet Baskonus, M. Nurul Islam, M. Ali Akbar and Danyal Soybaş

Abstract

The time-fractional generalized biological population model and the (2, 2, 2) Zakharov–Kuznetsov (ZK) equation are significant modeling equations to analyse biological population, ion-acoustic waves in plasma, electromagnetic waves, viscoelasticity waves, material science, probability and statistics, signal processing, etc. The new generalized G/G-expansion method is consistent, computer algebra friendly, worthwhile through yielding closed-form general soliton solutions in terms of trigonometric, rational and hyperbolic functions associated to subjective parameters. For the definite values of the parameters, some well-established and advanced solutions are accessible from the general solution. The solutions have been analysed by means of diagrams to understand the intricate internal structures. It can be asserted that the method can be used to compute solitary wave solutions to other fractional nonlinear differential equations by means of fractional complex transformation.


Corresponding author: Onur Alp Ilhan, Department of Mathematics, Faculty of Education, Erciyes University, 38039-Melikgazi, Kayseri, Turkey, E-mail:

Acknowledgement

The authors would like to express their gratitude to the anonymous referees for their helpful comments and suggestions to enhance the quality of the article.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-07-09
Revised: 2021-01-20
Accepted: 2021-02-07
Published Online: 2021-03-17

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