Exact Solutions for the Liénard Type Model via Fractional Homotopy Methods

  • V. F. Morales-Delgado
  • J. F. Gómez-AguilarEmail author
  • L. Torres
  • R. F. Escobar-Jiménez
  • M. A. Taneco-Hernandez
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 194)


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.


Fractional calculus Atangana–Baleanu fractional derivative Liénard type model 



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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • V. F. Morales-Delgado
    • 1
  • J. F. Gómez-Aguilar
    • 2
    Email author
  • L. Torres
    • 3
  • R. F. Escobar-Jiménez
    • 4
  • M. A. Taneco-Hernandez
    • 1
  1. 1.Facultad de MatemáticasUniversidad Autónoma de GuerreroChilpancingoMexico
  2. 2.CONACYT-Tecnológico Nacional de MéxicoCentro Nacional de Investigación y Desarrollo TecnológicoCuernavacaMéxico
  3. 3.CONACYT-Instituto de IngenieríaUniversidad Nacional Autónoma de MéxicoMéxico CityMéxico
  4. 4.Tecnológico Nacional de MéxicoCentro Nacional de Investigación y Desarrollo TecnológicoCuernavacaMéxico

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