Study On The Stability Of Two Fractional Order Systems

In this paper,the fractional-order exponential stability of the coupled system of Conformable fractional-order differential equations and the uniform stability of Riemann-Liouville(R-L)fractional-order time-varying time-delay inertial neural networks are studied respectively using the fractional-order calculus theory as a tool.The main research contents are as follows:Firstly,the fractional exponential stability of the coupled system of Conformable fractional differential equations is studied.Based on graph theory and Lyapunov method,a sufficient condition for the fractional exponential stability of the coupled system of Conformable fractional differential equations is derived by studying the Conformable derivative of Lyapunov function and using the combination properties of Conformable fractional derivative and integral.The rationality and validity of the proposed theory are further verified by numerical examples.The numerical simulation shows that the convergence speed of the system solution decreases with the decrease of the fractional order β(0＜β≤1).Secondly,R-L fractional-order time-varying inertial neural network is extended to R-L fractional-order time-varying inertial neural network,and the stability and synchronization of R-L fractional-order time-varying inertial neural network are studied.Based on the Lyapunov direct method,a Lyapunov-Krasovskii function containing R-L fractional integral is constructed.By using the combination property of R-L fractional derivative and integral,the first derivative of Lyapunov function is calculated,and the condition of uniform stability of R-L fractional order time-varying delay neural network model is deduced.Finally,the rationality and effectiveness of the uniform stability theory of the system are verified by numerical simulation.