A new application of the homotopy analysis method in solving the fractional Volterra's population system.
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.
Volterra's population system of fractional order
scientific article; zbMATH DE number 6362229