Existence And Stability Of Solutions For Several Kinds Of Fractional Differential Equations

Fractional calculus is an important part of the field of mathematics.Because of its significant contributions in many fields,including the chain breaking of polymer materials,automatic control theory,biomathematics,engineering and so on,it has aroused the great enthusiasm of scientific researchers for fractional calculus.This paper mainly studies the existence and stability of solutions of several types of fractional differential equations,which is divided into the following five chapters:The first chapter introduces the relevant research background,significance and development at home and abroad,as well as the relevant definitions and basic theories that need to be used in this paper.In chapter 2,by using a new estimation technique for the measure of noncompactness,the Sadovskii fixed point theorem and the Leray-Schauder fixed point theorem of condensation mapping,we study the existence of solutions for the following fractional differential equations with Sturm-Liouville boundary conditions in Banach space and give a example to illustrate the applicability of the obtained results.In chapter 3,we use the double variable Mittag-Leffler function to deduce the mild solution form of the following fractional stochastic differential equations and prove the existence and uniqueness of the solution.In addition,we also obtain and prove the constant variation formula corresponding to this differential equation.In chapter 4,we study the stochastic stability,almost surly exponential stability and pmoment exponential stability of the following conformable fractional stochastic differential equations by using the stopping time technique and the newly established It? formula of conformable version?and illustrate the applicability of the results.The fifth chapter is summary and prospect.