Stability Analysis For Some Kinds Of Fractional Differential Systems With Delay

In recent decades,fractional calculus in fluid mechanics,control theory,bioengineering and other fields are widely used.Because of its good genetic and memory characteristics,fractional order differential system can better describe the actual system.At the same time,during the in-depth study of the actual system,it was found that the system contains singular and delay factors,so the fractional differential system considering the singular and delay factors has important theoretical significance and research value.In this paper,the asymptotic stability of fractional neural networks with discrete and distributed delays,the global Mittag-Leffler stability of fractional nonlinear impulsive differential systems with delay and the stability of fractional singular perturbed systems are studied.The work of this paper mainly includes the following chapters:In the first chapter,the research background of this article is introduced,and then the main research contents and preliminary knowledge of this article are given.In the second chapter,we study the asymptotic stability of fractional neural networks with discrete and distributed delays in the sense of Caputo derivative.By constructing Lyapunov function and using fractional Razumikhin theorem,we give sufficient conditions for the asymptotic stability of fractional neural networks with discrete and distributed delays,and give two examples to verify the validity of the conditions.In the third chapter,we study the global Mittag-Leffler stability of fractional order nonlinear systems with impulsive and time-delay factors.By using the fractional Lyapunov method and the properties of Mittag-Leffler functions,we give the sufficient conditions for the global Mittag-Leffler stability of fractional order nonlinear systems with impulsive time-delay.Then,we prove the effectiveness of the results with concrete examples.In the fourth chapter,the stability of a class of fractional order singular perturbed systems is discussed.By using the Gronwall inequality,the sufficient conditions for the stability of fractional order singular perturbed systems are given,and the condition of the theorem is proved by an example.