  In this paper, an attempt is made to understand the dynamics of a fractional
order three species Leslie-Gower predator prey food chain model with simplified
Holling type IV functional response by considering fractional derivative in
Caputo Sense. First, we prove different mathematical results like existence,
uniqueness, non-negativity and boundedness of the solutions of fractional order
dynamical system. The dissipativeness of the solution of the FDE system is
discussed. Further, we investigate the Local stability criteria of all feasible
equilibrium points. Global stability of the interior equilibrium point have
also been discussed here. Using realistic parameter values, numerically it has
been observed that the fractional order system shows more complex dynamics,
like chaos as fractional order becomes larger. Analytical results are
illustrated with several examples in numerical section.
