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Exact Solutions for the Liénard Type Model via Fractional Homotopy Methods

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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, we present the solution for a Liénard type model of a pipeline expressed by Liouville–Caputo and Atangana-Baleanu-Caputo fractional order derivatives. For this model, new approximated analytical solutions are derived by using the Laplace homotopy perturbation method and the modified homotopy analysis transform method. Both the efficiency and the accuracy of the method are verified by comparing the obtained solutions versus the exact analytical solution.

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Acknowledgements

José Francisco Gómez Aguilar and Lizeth Torres acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014. José Francisco Gómez Aguilar, Lizeth Torres, Ricardo Fabricio Escobar Jiménez and Marco Antonio Taneco Hernández acknowledges the support provided by SNI-CONACyT.

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Chilpancingo, Guerrero, Mexico

    V. F. Morales-Delgado & M. A. Taneco-Hernandez

  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

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

    R. F. Escobar-Jiménez

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  1. V. F. Morales-Delgado
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  2. J. F. Gómez-Aguilar
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  3. L. Torres
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  4. R. F. Escobar-Jiménez
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  5. M. A. Taneco-Hernandez
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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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Morales-Delgado, V.F., Gómez-Aguilar, J.F., Torres, L., Escobar-Jiménez, R.F., Taneco-Hernandez, M.A. (2019). Exact Solutions for the Liénard Type Model via Fractional Homotopy Methods. 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_16

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  • DOI: https://doi.org/10.1007/978-3-030-11662-0_16

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