Stability And Boundedness Of Fractional Impulsive Differential Equations

Fractional differential equations have a wide range of applications in power fractal networks,hydrodynamics,rheology,viscoelasticity,anomalous diffusion,image processing,seismic analysis,transmission of biological systems,neural networks and many other fields,and are important research directions of differential equations theories and research hotsports.On the other hand,the continuous differential equation cannot accurately describe the change process of the complex reality problem,and the introduction of the impulse makes the fractional differential equation more close to the real problem,and can be more objective and accurate to solve the problem of disturbance caused by the change of the system caused by the sudden external disturbance.Therefore,it is necessary to investigate fractional impulsive differential equations in order to provide a rigorous mathematical theory for its practical applications.However,due to the difficulty of its research,theresearch on fractional impulsive differential equations is still deficient,especially about the boundedness of solutions.Based on this,the thesis aims to study the boundedness of solutions of fractional impulsive differential equations.This thesis is divided into five chapters:In the first chapter,the significance of the research on the stabilization of fractional impulsive differential equations is described.The development and research status of fractional differential systems and fractional differential equations are also introduced.The second chapter gives the related concepts and important lemmas for the stability and boundedness of Caputo fractional impulsive differential equations.The third chapter gives the main results,as well as the proof process of the stability and boundedness.The fourth chapter gives some examples and numerical simulations,showing the validity of the conclusion obtained in this paper on the stability and boundedness of fractional impulsive differential systems,and a summary of this chapter.The fifth chapter summarizes the main research results in the paper,and makes some suggestions for future research.