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New Fractional Modelling and Simulations of Prey–Predator System with Mittag–Leffler Kernel

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Abstract

Predator–prey models are regarded as the structural blocks of the bio- and ecosystems as biomasses are headed by their resource masses. During the current investigation, we examine the impact of a contagious disease on the growth of ecological varieties. We study a non-integer-order predator–prey system by applying the Atangana–Baleanu–Caputo derivative. We use an effective techniqueto get the numerical solutions and to discover the system’s dynamical behavior using different values of fractional order which indicates that how how the proposed scheme is suitable to solve the dynamical systems containing the derivatives with non-singular kernels. Moreover, the existence of the results is given utilizing the fixed-point theorem. Also, diagrams via numerical simulations of the approximate solutions are shown in different dimensions.

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Acknowledgements

The authors would like to thank the reviewers for their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Clarkson University, Potsdam, NY, 13699, USA

    Mohammad Partohaghighi

  2. Art and Science Faculty, Department of Mathematics, Siirt University, 56100, Siirt, Turkey

    Ali Akgül

  3. Department of Electronics and Communication Engineering, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India

    Ali Akgül

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Partohaghighi, M., Akgül, A. New Fractional Modelling and Simulations of Prey–Predator System with Mittag–Leffler Kernel. Int. J. Appl. Comput. Math 9, 43 (2023). https://doi.org/10.1007/s40819-023-01523-5

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