A sincGaussJacobi collocation method for solving Volterra's population growth model with fractional order
Abbas Saadatmandi$^1$, Ali Khani$^2$ and MohammadReza Azizi$^3$
A new sincGaussJacobi collocation method for
solving the fractional Volterra's population growth model in a
closed system is proposed. This model is a nonlinear fractional
Volterra integrodifferential equation where the integral term
represents the effects of toxin. The fractional derivative is
considered in the LiouvilleCaputo 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 GaussJacobi
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 wellknown results in the
literature to show the applicability and efficiency of the proposed
method.
Tbilisi Mathematical Journal, Vol. 11(2) (2018), pp. 123–137
