Tbilisi Mathematical Journal

A sinc-Gauss-Jacobi collocation method for solving Volterra's population growth model with fractional order

Abbas Saadatmandi, Ali Khani, and Mohammad-Reza Azizi

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Abstract

A new sinc-Gauss-Jacobi collocation method for solving the fractional Volterra's population growth model in a closed system is proposed. This model is a nonlinear fractional Volterra integro-differential equation where the integral term represents the effects of toxin. The fractional derivative is considered in the Liouville-Caputo sense. In the proposed method, we first convert fractional Volterra's population model to an equivalent nonlinear fractional differential equation, and then the resulting problem is solved using collocation method. The proposed collocation technique is based on sinc functions and Gauss-Jacobi quadrature rule. In this approach, the problem is reduced to a set of algebraic equations. The obtained numerical results of the present method are compared with some well-known results in the literature to show the applicability and efficiency of the proposed method.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 2 (2018), 123-137.

Dates
Received: 6 August 2017
Accepted: 25 March 2018
First available in Project Euclid: 20 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1529460027

Subjects
Primary: 65M70: Spectral, collocation and related methods
Secondary: 26A33: Fractional derivatives and integrals 92D40: Ecology

Keywords
collocation method fractional derivatives and integrals sinc functions Volterra’s population Liouville-Caputo derivative

Citation

Saadatmandi, Abbas; Khani, Ali; Azizi, Mohammad-Reza. A sinc-Gauss-Jacobi collocation method for solving Volterra's population growth model with fractional order. Tbilisi Math. J. 11 (2018), no. 2, 123--137. https://projecteuclid.org/euclid.tbilisi/1529460027


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