A new application of the homotopy analysis method in solving the fractional Volterra's population system.
type: Item
instance of: scholarly article
title: A new application of the homotopy analysis method in solving the fractional Volterra's population system.
zbMATH Open document ID: 1340.26016
author: M. Ghasemi
author: M. Fardi
author: Reza Khoshsiar Ghaziani
published in: Applications of Mathematics
publication date: 2014-10-29T00:00:00Z
full work available at URL: http://hdl.handle.net/10338.dmlcz/143775
review text: The paper suggests numerical strategies to obtain approximate solutions of the fractional population growth model of the form \(D^{\alpha}p(t)=ap(t)-bp^2(t)-cp(t)\int_0^tp(s)ds\), \(p(0)=p_0\), \(0<\alpha\leq 1.\) Here the fractional derivative \(D^{\alpha}\) is considered in the Caputo sense. After some preliminaries in Section 2, the authors apply a homotopy analysis method (in Section 3), which leads to a two parameter form of the numerical solutions. The paper closes with some numerical results when \(\alpha=0.3\) and \(\alpha=0.5\) and the parameters take some concrete values.
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6362229
zbMATH Keywords: fractional derivatives
zbMATH Keywords: fractional integrals
zbMATH Keywords: fractional population model
zbMATH Keywords: homotopy analysis method
zbMATH Keywords: Volterra's population system of fractional order
zbMATH Keywords: Caputo's fractional derivative
zbMATH Keywords: bi-parametric homotopy method
zbMATH Keywords: convergence region
reviewed by: George Karakostas
MaRDI profile type: Publication
OpenAlex ID: W2028885994
cites work: Numerical approximations for population growth models
cites work: Algorithms for the fractional calculus: a selection of numerical methods
cites work: Approximate analytical solution for seepage flow with fractional derivatives in porous media
cites work: Q4941485
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Q4438574
cites work: Vito Volterra and theoretical ecology
cites work: Classroom Note:Numerical and Analytical Solutions of Volterra's Population Model
cites work: Analytical approximations and Padé approximants for Volterra's population model
DOI: 10.1007/S10492-014-0057-3
description: scientific article; zbMATH DE number 6362229