Analysis of logistic equation pertaining to a new fractional derivative with non-singular kernel

Abstract

In this work, we aim to analyze the logistic equation with a new derivative of fractional order termed in Caputo–Fabrizio sense. The logistic equation describes the population growth of species. The existence of the solution is shown with the help of the fixed-point theory. A deep analysis of the existence and uniqueness of the solution is discussed. The numerical simulation is conducted with the help of the iterative technique. Some numerical simulations are also given graphically to observe the effects of the fractional order derivative on the growth of population.