Numerical method for transient solution of the fractional logistic differential equation in population growth model

Abstract

In many cases, the order of a differential equation is a natural number. However, in some applications, this order can be in the form of a fractional number, so that the equation is then called a fractional differential equation. In this paper, we study the numerical solution of the fractional logistic differential equation with order α, where 0 < α ≤ 1. The equation can be considered as one of the fractional Riccati differential equations. The numerical methods we use are the Adomian decomposition method (ADM) and the variational iteration method (VIM). We use the Caputo derivative to find the solution. The effect of the fractional-order into the transient solution is studied graphically to find the interpretation in the logistic population growth model.