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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Fuzzy Fractional Predator-Prey Model: A Numerical Approach Using Fuzzy Fractional Fourth Order Runge-Kutta Method

Discontinuity, Nonlinearity, and Complexity 15(4) (2026) 579--595 | DOI:10.5890/DNC.2026.12.008

S. Luvis Savla$^{1}$, R. Gethsi Sharmila$^{1}$, T. Kanna$^{2}$

$^{1}$ PG & Research Department of Mathematics, Bishop Heber College (Affiliated to Bharathidasan University), Tiruchirappalli- 620017, India

$^{2}$ Nonlinear Waves Research Lab, PG & Research Department of Physics, Bishop Heber College (Affiliated to Bharathidasan University), Tiruchirappalli- 620017, India

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Abstract

We consider a fractional predator-prey system under the Caputo fractional derivative describing ecological mathematical models in the presence of environmental influences like the Allee effect, fear effect, and immigration. Particularly, this system arises in the context of interacting animals. We formulate the approximate method namely, fuzzy fractional fourth order Runge-Kutta method (FFRK4) to the underlying system of fuzzy fractional nonlinear differential equations. This approach enables us to study the fractional system over a range of initial values. Our study reveals non-trivial growth rate in fuzzy fractional predator-prey system. The results of the model indicate that this method is effective and easy to use in Fuzzy Fractional Differential Equation (FFDE) systems.

Acknowledgments

T.K. acknowledges the support received from SERB, Department of Science and Technology, Government of India, through a Core Research Grant (Grant No. CRG/2021/004119). I am also grateful to Dr. P. Prakash, Assistant Professor, Department of Mathematics, Amrita School of Engineering, Coimbatore for carefully reviewing the work and offering valuable suggestions that helped improve its overall structure and argumentation.

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