Travelling waves solution for fractional-order biological population model

Hassan Khan¹ ; Rasool Shah¹ ; J.F. Gómez-Aguilar^2, 3 ; Shoaib¹ ; Dumitru Baleanu^4, 5, 6 ; Poom Kumam^7, 8

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.

Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 32

Résumé

In this paper, we implemented the generalized and extended 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 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.

Détail

DOI : 10.1051/mmnp/2021016

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