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Parameter Estimation of Fractional Gompertz Model Using Cuckoo Search Algorithm

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Fractional Derivatives with Mittag-Leffler Kernel

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 194))

Abstract

In this chapter, a meta-heuristic optimization algorithm, called cuckoo search algorithm is applied to determine the optimal parameters of the fractional Gompertz model via Liouville–Caputo and Atangana–Baleanu–Caputo fractional derivatives. The numerical solutions of the proposed models were obtained using the Adams method. The proposed methodology is tested on epidemiological examples. In the interval considered, the fractional models had the best fit for the epidemiological data considered. The effectiveness of the methodology is shown by a comparison with the classical models. A comparison between the fractional models and the classical models was carried out to show the effectiveness of our methodology.

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Acknowledgements

Jesús Emmanuel Solís Pérez acknowledges the support provided by CONACyT through the assignment doctoral fellowship. José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014. José Francisco Gómez Aguilar and Ricardo Fabricio Escobar Jiménez acknowledges the support provided by SNI-CONACyT.

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Authors and Affiliations

  1. Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Interna del Internado, Palmira, 62490, Cuernavaca, Morelos, México

    J. E. Solís-Pérez, R. F. Escobar-Jiménez & V. H. Olivares-Peregrino

  2. CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Interna del Internado, Palmira, 62490, Cuernavaca, Morelos, México

    J. F. Gómez-Aguilar

  3. CONACYT-Instituto de Ingeniería, Universidad Nacional Autónoma de México, México City, México

    L. Torres

Authors
  1. J. E. Solís-Pérez
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  2. J. F. Gómez-Aguilar
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  3. R. F. Escobar-Jiménez
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  4. L. Torres
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  5. V. H. Olivares-Peregrino
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Corresponding author

Correspondence to J. F. Gómez-Aguilar .

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Editors and Affiliations

  1. CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, Mexico

    José Francisco Gómez

  2. CONACYT-Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Lizeth Torres

  3. Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, Mexico

    Ricardo Fabricio Escobar

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Solís-Pérez, J.E., Gómez-Aguilar, J.F., Escobar-Jiménez, R.F., Torres, L., Olivares-Peregrino, V.H. (2019). Parameter Estimation of Fractional Gompertz Model Using Cuckoo Search Algorithm. In: Gómez, J., Torres, L., Escobar, R. (eds) Fractional Derivatives with Mittag-Leffler Kernel. Studies in Systems, Decision and Control, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-030-11662-0_6

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  • DOI: https://doi.org/10.1007/978-3-030-11662-0_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11661-3

  • Online ISBN: 978-3-030-11662-0

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