On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

Abstract

This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using Matlab-16, we simulate the series solution to illustrate our results graphically. Finally, a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.