The Study On Solutions Of Two Classes Of Nonlinear Fractional Differential Coupled Systems With Impulses

Fractional differential coupled systems as the mathematical models have been widely used to describe phenomena and processes in a lot of fields,in result of some experimental results show that the fractional order differential coupled systems models are more accurate than the integer order's.Moreover,it is well known that the effects of pulse are inevitable in many phenomena and processes.Therefore,fractional differential coupled systems have raised extensive attention and research in recent few decades,and in particular,boundary value problems for fractional order differential coupled systems with impulses have been studied and developed more extensively.Thus,this thesis mainly studies the solutions of two classes of nonlinear fractional differential coupled systems with impulses.The main contents of this thesis are as follows:The first chapter mainly introduces the background of this thesis,the research status.At the same time,the related concepts?definitions?theorems of fractional calculus and the arrangement of this thesis are introduced.The second chapter studies the boundary value problem of a class of nonlinear fractional differential coupled system with impulses,by means of the Banach contraction principle and the Schauder fixed point theorem,some sufficient criteria are established to guarantee the uniqueness and existence of solutions of the boundary value problem of coupled system.In third chapter researches a class of nonlinear impulsive neutral fractional differential coupled system with infinite delay,by means of the Banach contraction principle and the Krasnoselskii fixed point theorem,some sufficient criteria are established to guarantee the uniqueness and existence of solutions of coupled system.In the fourth chapter,we make a brief summary and prospect for this thesis.