A new numerical scheme applied on re-visited nonlinear model of predator-prey based on derivative with non-local and non-singular kernel

Badr Saad T. Alkahtani; Ilknur Koca

doi:10.3934/dcdss.2020024

Article Contents

2020, Volume 13, Issue 3: 429-442. Doi: 10.3934/dcdss.2020024

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A new numerical scheme applied on re-visited nonlinear model of predator-prey based on derivative with non-local and non-singular kernel

Badr Saad T. Alkahtani^1, and
Ilknur Koca^2,

1.
Department of mathematics, Riyadh, 11989, colle of science, King Saud University, P.O. Box 1142, Saudi Arabia
2.
Mehmet Akif Ersoy University, Department of Mathematics, Faculty of Sciences, 15100, Burdur, Turkey

Received: April 30, 2018

Revised: April 30, 2018

Published: December 2019

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Abstract

A new concept of dynamical system of predator-prey model is presented in this paper. The model takes into account the memory of interaction between the prey and predator due to the inclusion of fractional differentiation. In addition, the model takes into account the inherent disposition of a prey or predator toward hunting or defending in time. Analysis of existence and uniqueness of the solutions is presented. A numerical method is used to generate some simulations as the fractional orders change from one to zero. A new traveling waves patterns are obtained.

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Mathematics Subject Classification: Primary: 34A34, 47H10, 65L07; Secondary: 47N40.

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Figure 1. Numerical solution for $ \alpha = 0.05. $

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Figure 2. Numerical solution for $ \alpha = 0.5. $

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Figure 3. Numerical solution for $ \alpha = 0.8. $

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Figure 4. Numerical solution for $ \alpha = 1. $

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References

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