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Numerical solution of fractal-fractional Mittag–Leffler differential equations with variable-order using artificial neural networks

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Abstract

In this work, a methodology based on a neural network to solve fractal-fractional differential equations with a nonsingular and nonlocal kernel is proposed, the neural network is optimized by the Levenberg–Marquardt algorithm. For evaluating the neural network, different chaotic oscillators of variable order are solved and compared with algorithms of numeric approximation.

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Acknowledgements

José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT. The Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia funded this project, under Grant no. (FP-110-42).

Author information

Authors and Affiliations

  1. Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, MOR, Mexico

    C. J. Zúñiga-Aguilar & R. F. Escobar-Jiménez

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

    J. F. Gómez-Aguilar

  3. Université Grenoble Alpes, Grenoble, 38000, France

    H. M. Romero-Ugalde

  4. CEA LETI MINATEC Campus, Grenoble, 38054, France

    H. M. Romero-Ugalde

  5. Departamento de Física y Matemáticas., Universidad Iberoamericana, 01219, Mexico, CDMX, Mexico

    G. Fernández-Anaya

  6. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia

    Fawaz E. Alsaadi

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  1. C. J. Zúñiga-Aguilar
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All authors have contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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Correspondence to J. F. Gómez-Aguilar.

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Zúñiga-Aguilar, C.J., Gómez-Aguilar, J.F., Romero-Ugalde, H.M. et al. Numerical solution of fractal-fractional Mittag–Leffler differential equations with variable-order using artificial neural networks. Engineering with Computers 38, 2669–2682 (2022). https://doi.org/10.1007/s00366-020-01229-y

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