Abstract
The essential target of this work is to analyse the dynamical behaviour of the arbitrary order eco - epidemiological model by adopting the new numerical method. We applied the power law kernel, exponential decay kernel, and generalized Mittag-Leffler kernel functions for treatment of arbitrary order eco-epidemiological model where the considered eco-epidemiological model is a non-linear dynamical system with three population species. Further, we calculated the uniqueness and existence of the solutions by adopting the fixed point hypothesize. Further, we studied the stability analysis for aforesaid model. We examine the possibility for finding new dynamical phase portraits with singular and non-singular arbitrary order operator and demonstrate the dynamical phase portraits at various values of arbitrary order. Furthermore, we have found out the maximal bifurcation graph of the eco-epidemiological system and this eco-epidemiological model is numerically solved by adopting Atangana-Seda (AS) numerical method. We have used Newton's polynomial.