A study on fractional host–parasitoid population dynamical model to describe insect species

The parasitoid is a broad evolutionary association of hymenopteran insects which are well-known as biological control agents. Parasites are different from predators because parasites only take resources from one host, whereas predators eat many preys. The preeminent target of this study is to present a fractional model of host–parasitoid population dynamical system through the Caputo operator. The host–parasitoid population dynamical model is a system of three dimensional coupled differential equations. This research also investigates the possibility for obtaining new chaotic behaviors with singular fractional operator and shows the chaotic behavior at different values of fractional order. Furthermore, two numerical schemes Adam–Bashforth–Moulton and new Toufik–Atangana mechanism were suggested to solve fractional host–parasitoid population numerically. Again, some numerical simulations are perform to assess the efficiency of the newly proposed method. Some attractive illustration is presented through graphically. We strongly believe that the proposed work will open various new doors of investigations toward modeling on parasitoid.