In the current research work, fractional version of logistic differential model is studied with Allee effect which includes a threshold population. It also initial conditions. The definition derivative utilised in this Caputo-Fabrizio. order to give solution posed problem by an implicit representation, method based on properties used.

Abstract In this paper, we study the numerical solutions of Fisher’s equation and to a nonlinear diffusion equation of the Fisher type by differential quadrature method. Fisher's equation combines diffusion with logistic nonlinearity. The equation occurs in logistic population growth models, neurophysiology and nuclear reactions. Therefore, numerical study of these types of equations is very im...

For a certain class of neutral differential equations it is shown that these equations can serve as population models in the sense that they can be interpreted as special cases or caricatures of the standard Gurtin-MacCamy model for a population structured by age with birth and death rate depending on the total adult population. The delayed logistic equation does not belong to this class but th...