| In this paper,several classes of fractional neutral neural networks are studied.By using fixed point theory,some properties and inequalities of fractional differential function,the existence and uniqueness of solution,generalized Mittag-Leffler stability and asymptotic stability in pth moment are established.In the first part,it is introduced for the special function,Mittag-Leffler function,to transform the differential equations into integral equations.Subsequently,employing the Banach fixed point theory in two distinct complete probability spaces,we prove the pth moment asymptotic stability of fractional neutral neural network systems with time delays and Poisson jumps,as well as the pth moment generalized Mittag-Leffler stability of systems without Poisson jumps.What’s more,the validity of the results is verified by selecting a set of numerical simulations.In the second part,the stability and existence of solutions for a class of undisturbed system is studied.First,by using fixed point theory,the asymptotic stability and generalized Mittag-Leffler stability are established.Then,the existence and uniqueness of solutions are proved in a weighted continuous function space.The validity of the results is verified by numerical simulations.At the end of the paper,the work of this paper is summarized and some problems which can be further discussed in the future are given. |
