Analyzing predator-prey dynamics in the context of global warming using fractional integro differential equations

Volume 39, Issue 2, pp 249--262 https://dx.doi.org/10.22436/jmcs.039.02.05

Publication Date: March 29, 2025 Submission Date: July 16, 2024 Revision Date: November 02, 2024 Accteptance Date: January 16, 2025

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Authors

K. S. Nisar - Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia. - Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Jordan. G. Hamsavarthini - Department of Mathematics, Kongunadu Arts and Science College, Coimbatore-641 029, India. C. Ravichandran - Department of Mathematics, Kongunadu Arts and Science College, Coimbatore-641 029, India. Sh. U. Kumaran - Department of Mathematics and Statistics, Providence Women's College, Malaparamba, Kozhikode-673 009, India.

Abstract

In the field of ecology, the primary focus is on how climate change induced environmental shifts, including increasing temperatures, influence the relationships between species. This study presents a model that we have created to simulate the interactions between two species; one being a predator and the other its prey. In the context of the current situation, we propose using a fractional integro differential model, in line with Caputo's method. The existence of solutions is confirmed, and their stability is analyzed and the existence of unique solution is demonstrated with an example. Finally, the numerical results are plotted to show how memory effects affect ecological stability over time using iterative population estimates.

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Keywords

• Fractional calculus
• mathematical global warming model
• prey-predator
• fixed point
• stability results
• numerical methods

MSC

•  26A33
•  86A08
•  37C25
•  45M10
•  65R10

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