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A new application of the homotopy analysis method in solving the fractional Volterra’s population system

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Abstract

This paper considers a Volterra’s population system of fractional order and describes a bi-parametric homotopy analysis method for solving this system. The homotopy method offers a possibility to increase the convergence region of the series solution. Two examples are presented to illustrate the convergence and accuracy of the method to the solution. Further, we define the averaged residual error to show that the obtained results have reasonable accuracy.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

    Mehdi Ghasemi

  2. Department of Mathematics, Islamic Azad University, Najafabad Branch, Najafabad, Iran

    Mojtaba Fardi

  3. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

    Reza Khoshsiar Ghaziani

Authors
  1. Mehdi Ghasemi
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  2. Mojtaba Fardi
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  3. Reza Khoshsiar Ghaziani
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Corresponding author

Correspondence to Mojtaba Fardi.

Additional information

This research was partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Iran.

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Ghasemi, M., Fardi, M. & Ghaziani, R.K. A new application of the homotopy analysis method in solving the fractional Volterra’s population system. Appl Math 59, 319–330 (2014). https://doi.org/10.1007/s10492-014-0057-3

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  • DOI: https://doi.org/10.1007/s10492-014-0057-3

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