Existence And Uniqueness Of The Solution?Stability And Admissibility Of Fractional Differential Systems

With the development and requirement of social science technology and modern industry,it becomes one of the most significant issues to constantly improve the accuracy and authenticity of mathematical models.Indeed,the dynamic process of most practical systems are fractional,such as electromagnetic wave conductance,viscoelasticity systems,fluid mechanics,biological systems,etc.For these systems,we must use fractional differential equation to describe them on account of the demand of more accurate analysis and synthesis.At the same time,the delay and singular is also the common phenomenon in practical systems.Therefore,it is of important theory value and practical meaning to study the fractional differential system with time delay and singular.There are five chapters in this thesis.The Chapter 1 is introduction.This chapter mainly introduce the research background of this thesis.The Chapter 2 is preparatory knowledge.This chapter gives the basic knowledge about the fractional calculus and singular control systems as well as the commonly used lemmas.The Chapter 3 is the existence and uniqueness of the solution of fractional damped dynam-ical systems.This chapter gives several sufficient conditions for the existence of the solution.The Chapter 4 is finite-time stability of fractional differential singular delay systems.This chapter gives the sufficient condition of the finite-time stability of fractional differential singular delay systems.The Chapter 5 is admissibility of fractional differential systems.This chapter gives the sufficient and-necessary condition of the admissibility of fractional differential system with order a belong to the interval from one to two.