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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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
Keywords
- Volterra’s population system of fractional order
- Caputo’s fractional derivative
- bi-parametric homotopy method
- convergence region