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

Abbas Saadatmandi$^1$, Ali Khani$^2$ and Mohammad-Reza Azizi$^3$

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.

Tbilisi Mathematical Journal, Vol. 11(2) (2018), pp. 123137