Numerical Studies For Fractional-Order Logistic Differential Equation With Two Different Time Delays

With the great progress of science and technology, the research of natural phenomena and social phenomenon is much more subtle today. When we entered the complex phenomenon and the research of complex systems, the classical integer order differential equation will have some problems, so the fractional order differential equations was born suitably. The fractional order differential equation is suitable to describe material and process that have memory and genetic properties. And for the description of the complex phenomena and system, its superiority is that it makes the description model with simple parameters, has clear physical meaning, has accurate description and so on. Therefore, fractional order differential equation becomes one of the important mathematical modeling tools of the complex mechanics and physical process.Sometimes it is hard to use an ordinary differential equation to describe many problems clearly. Because a lot of practical problems are not only related to the present state, and may involve future state or even the state of the past. In consideration of this kind of complicated situations, we need to look for a new mathematical model to describe and solve the practical problems.In this paper we try to consider some problem in which the present states and the previous states are both considered. The differential equation with time delay are considered to describe the real world problems. Here the states at present, in the past, and in the future, or even in a more complicated time state had been taken into account. And some method in control theory of the differential equation with time delay are used to solve the problem.