Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

Abstract The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey–predator model with imprecise biological parameters and fractional order generalized Hukuhara (fgH) differentiability. In this vain, different possible systems of the model are constructed, according to the increasing and decreasing behavior of population growth. Feasibility and stability analyses of equilibrium points of the stated models are also discussed by means of variational matrix with Routh–Hurwitz conditions. In addition, the numerical elaborations are carried out by taking parametric expansion of fuzzy fractional Laplace transform (FFLT). This significantly helps the researchers in using a novel approach to analyze the constant solutions of the dynamical systems in the presence of fractional index. This would allow the avoidance of any intricacy that occurs while solving fractional order derivatives. Furthermore, this attempt also provides numerical and pictorial results, obtained through some well-known methods, namely fifth-forth Runge–Kutta method (FFRK), Grunwald–Letnikov’s definition (GL) and Adams–Bashforth method (ABM) that are deemed appropriate to scrutinize the dynamics of the system of equations.

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