Issue |
Math. Model. Nat. Phenom.
Volume 16, 2021
Fractional Dynamics in Natural Phenomena
|
|
---|---|---|
Article Number | 32 | |
Number of page(s) | 24 | |
DOI | https://doi.org/10.1051/mmnp/2021016 | |
Published online | 04 June 2021 |
Travelling waves solution for fractional-order biological population model
1
Department of Mathematics. Abdul Wali Khan University Mardan (AWKUM), Pakistan.
2
CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490,
Cuernavaca Morelos, México
3
Consejo Académico, Universidad Virtual CNCI,
Monterrey, México.
4
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University,
06530
Ankara, Turkey.
5
Institute of Space Sciences,
Magurele-Bucharest, Romania.
6
Department of Medical Research, China Medical University Hospital, China Medical University,
Taichung,
Taiwan, Republic of China.
7
Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod,
Thung Khru,
Bangkok
10140, Thailand.
8
Department of Medical Research, China Medical University Hospital, China Medical University,
Taichung
40402, Taiwan.
* Corresponding author: jgomez@cenidet.edu.mx
Received:
11
December
2020
Accepted:
19
March
2021
In this paper, we implemented the generalized (G′/G) and extended (G′/G) methods to solve fractional-order biological population models. The fractional-order derivatives are represented by the Caputo operator. The solutions of some illustrative examples are presented to show the validity of the proposed method. First, the transformation is used to reduce the given problem into ordinary differential equations. The ordinary differential equation is than solve by using modified (G′/G) method. Different families of traveling waves solutions are constructed to explain the different physical behavior of the targeted problems. Three important solutions, hyperbolic, rational and periodic, are investigated by using the proposed techniques. The obtained solutions within different classes have provided effective information about the targeted physical procedures. In conclusion, the present techniques are considered the best tools to analyze different families of solutions for any fractional-order problem.
Mathematics Subject Classification: 34A34 / 35A20 / 35A22 / 44A10 / 33B15
Key words: Extended (G′/G)-expansion method / generalized (G′/G)-expansion method / fractional-order biological population models / traveling wave solutions / Riemann-Liouville’s derivative / complex transformation
© The authors. Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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