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**Iterative methods for a fractional-order Volterra population model.**
*(English)*
Zbl 1435.45002

Summary: We prove an existence and uniqueness theorem for a fractional-order Volterra population model via an efficient monotone iterative scheme. By coupling a spectral method with the proposed iterative scheme, the fractional-order integrodifferential equation is solved numerically. The numerical experiments show that the proposed iterative scheme is more efficient than an existing iterative scheme in the literature, the convergence of which is very sensitive to various parameters, including the fractional order of the derivative. The spectral method based on our proposed iterative scheme shows greater flexibility with respect to various parameters. Sufficient conditions are provided to select the initial guess that ensures the quadratic convergence of the quasilinearization scheme.

### MSC:

45D05 | Volterra integral equations |

45J05 | Integro-ordinary differential equations |

47J25 | Iterative procedures involving nonlinear operators |

34A08 | Fractional ordinary differential equations |

92D25 | Population dynamics (general) |

65R20 | Numerical methods for integral equations |

### Keywords:

Caputo’s fractional derivative; monotone iterative technique; quasilinearization; spectral collocation method; Volterra population model
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\textit{R. Roy} et al., J. Integral Equations Appl. 31, No. 2, 245--264 (2019; Zbl 1435.45002)

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