Executive Summary : | Mathematical ecology and its challenges are very important worldwide concern due to very high complexity of ecological systems and transient nature of environmental conditions. Mathematical modeling of ecological system plays a vital role in the form of mathematical models, to address the problem arising in population dynamics. The increasing study of realistic mathematical models in population dynamics is a reaction of their use to understand the concepts, tools and techniques, dynamical processes and predictions. Recently, the researchers are using fractional-order differential equations to understand the dynamical behavior of interacting population. The main advantages of this tool over classical ordinary differential equations are that, it describe the hereditary property of various biological elements and has a lot of similarities to fractals. Mathematical modeling is a useful technique for analyzing a variety of complicated biological problems. Generally, we use integer order derivatives for modeling the predator-prey system. We will design different mathematical model using fractional-order differential equations, and a unified framework to understand the complex dynamical behavior of interacting population. We will identify the ranges of the biologically realistic parameter values for the dynamical system. |