Stability For Non-local And Non-autonomous Fractional Order Differential Systems With Delays

The existence,uniqueness of the solutions to IVP(initial value problems)and stability of differential systems are the core matters of the differential system's research.The IVP and BVP(boundary value problems)of fractional order differential systems are worth further researching.Basing on predecessors' work and the guiding of the Riemann-Liouville fractional order derivative,we studied the nonlinear systems with non-local,non-autonomous and delays.In this paper,we mainly studied the existence,uniqueness of the solutions and stability of differential systems.The main contents are as follows:In chapter one,we introduced the background and the results have been studied of the nonlocal and non-autonomous Riemann-Liouville type fractional order differential systems with delays.In chapter two,we studied the existence and uniqueness of the solutions of the following systems:where the D? denotes ? order Riemann-Liouville derivative;0<p<1.Firstly,by the integral method,we transformed the problem into Volterra integral equivalent form.Then,by the Banach fixed point theorem,we testified the existence and uniqueness of the solutions.In chapter three,we generalized the finite time stability concept to nonlinear sys-tems.By using fractional generalized Gronwall inequality,we proved the finite time stability of this system.Then the stability was proved under the meaning ofIn chapter four,this paper was summarized and prospected.