Finite-Time Synchronization And Projection Synchronization Of Fractional-order Neural Networks With Time Delay

In this paper,a classical model-fractional time-delay neural network system is selected.Firstly,an inequality about the rising function is proposed based on Holder inequality.Then in the case of 1<? <2,in order to make the driving system and the corresponding response system synchronize in a finite time.We first define an error system,then by using Jensen's inequality,generalized Gronwall inequality and linear feedback controller.A sufficient criterion is established,it ensures that this kind of fractional-order neural network system with time delay can realize finite-time synchronization.Finally,this criterion is verified to be reasonable by Matlab exercise.Next,we extended the real-valued system to the complex-valued system.Without decomposing the complex-valued system into two real-valued systems,in the same way,when the order is 0 <? <1,in order to promote the drive-response system to achieve projection synchronization in a finite time.Firstly,we define the error system,design two new controllers,and construct the Lyapunov function.Using feedback controller,adaptive controller and various inequalities,it derives two different criteria,the projection synchronization is successfully completed.Further,we can effectively estimate the synchronization time,which is related to the fractional derivative and control parameters.Finally,two numerical cases are given to prove the validity and feasibility of the results.