Research Article Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model Noor S. Sh. Barhoom and Sadiq Al-Nassir Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq Correspondence should be addressed to Sadiq Al-Nassir; sadiq.n@sc.uobaghdad.edu.iq Received 14 September 2021; Revised 21 October 2021; Accepted 27 November 2021; Published 15 December 2021 Academic Editor: Jaume Giné Copyright © 2021 Noor S. Sh. Barhoom and Sadiq Al-Nassir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model. 1. Introduction The most influential theme in ecology and mathematical modeling is the dynamic of the relationship among species. Many authors extended or modified the work of the Lotka and Voltera model [1, 2], and they have investigated thse topics widely by using ordinary differential equations or def- erence equations, see [3–9], and references therein. Nowa- days, authors formulate their mathematical models by fractional order differential equation due to their ability to give the precise description for various linear and nonlinear phenomena [10–15]. The increasing of mathematical models that based on fractional order differential equation has recently obtained popularity in the studying the behavior of biological models. Fractional-order differential equation has been successfully used and applied to model many areas of science, engineering, and phenomena that cannot be for- mulated by other types of equations [10, 16]. In [12, 16–21], authors have investigated the effects of the fractional order differential equation on a prey predator model as well as they also discussed the stability analysis of equilibrium points of fractional order model with and without harvest- ing, as well as the existence, uniqueness, and boundedness of the solutions that are proved. There are several different types of definitions of fractional-order differential equation in the literatures [16, 22–25], for e.g., Caputo, Riemann-Litouville, Fabrizio, Mar- echand,Grunwald-Letnikov, wayl, and Riesz fractional-order derivatives. Throughout this work, we used the Caputo fractional-order derivatives because it is not necessary to define the initial conditions of fractional-order and its fractional-order derivative of constant function is zero, as well as the similarity of the initial conditions of fractional order differential and the integer order ones [8]. This work is organized as follows: in Section 2, some useful definitions and concept that concern to the fractional order are pre- sented. In Section 3, a three-dimensional fractional-order prey-predator model is considered. The uniqueness and boundedness as well as the nonnegativity of its solution are proved. In Section 4, all the equilibrium points are deter- mined, and the conditions to achieve its local stability are set. In Section 5, numerical simulations are given to confirm the theoretical results. Finally, conclusions are given in Sec- tion 6. Hindawi Abstract and Applied Analysis Volume 2021, Article ID 1366797, 10 pages https://doi.org/10.1155/2021/1366797