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Two efficient numerical schemes for simulating dynamical systems and capturing chaotic behaviors with Mittag–Leffler memory

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Abstract

In this paper, we consider two accurate iterative methods for solving fractional differential equations with power law and Mittag–Leffler kernel. We focused our attention on the stage-structured prey–predator model and several chaotic attractors of type Newton–Leipnik, Rabinovich–Fabrikant, Dadras, Aizawa, Thomas’ and 4 wings. The first algorithm is based on the trapezoidal product-integration rule, and the second one is based on Lagrange interpolations. The results obtained show that both numerical methods are very efficient and provide precise and outstanding results to determine approximate numerical solutions of fractional differential equations with non-local singular kernels.

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Acknowledgements

José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

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Authors and Affiliations

  1. Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran

    Behzad Ghanbari

  2. Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahcesehir University, 34349, Istanbul, Turkey

    Behzad Ghanbari

  3. CONACyT-Tecnológico Nacional de México/CENIDET., Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

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  1. Behzad Ghanbari
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Correspondence to J. F. Gómez-Aguilar.

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Ghanbari, B., Gómez-Aguilar, J.F. Two efficient numerical schemes for simulating dynamical systems and capturing chaotic behaviors with Mittag–Leffler memory. Engineering with Computers 38, 2139–2167 (2022). https://doi.org/10.1007/s00366-020-01170-0

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