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A numerical analysis for fractional model of the spread of pests in tea plants

Abstract In this study, we commenced an arbitrary order mathematical system of the tritrophic food chain population consisting of the host, pest, and predator to analyze the various field observations through Caputo's operator. The tritrophic population dynamical model is a system of three‐dimensional coupled differential equations. Further, this research also investigates the possibility for obtaining new chaotic behaviors with singular fractional operator and shows the chaotic behavior at various values of arbitrary order. Stability analysis of recommended numerical scheme is presented for suggested system. The existence and uniqueness results of the numerical solution of the suggested system are investigated. Moreover, we have derived the bifurcation diagrams by varying parameter a. Further, two numerical schemes Toufik–Atangana technique based on Lagrange polynomial piece‐wise interpolation and new numerical method based on Newton polynomial were suggested to solve arbitrary order tritrophic food chain population numerically. Again, some numerical simulations are performing to access the adaptability of the newly suggested methods. Some attractive illustrations are presented through graphically.

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