Study On Qualitative Properties Of Solutions Of Some Fractional Differential Equations

With the research on the theory and application of fractional calculus,the qualitative properties of fractional differential equations have become one of the hot research directions,such as the existence,uniqueness,boundedness,oscillation,asymptotics of solutions and the corresponding Fractional Inequalities.Among them,the research on the existence and uniqueness of solutions of boundary value problems of fractional differential equations has also produced a series of results.As a powerful tool of qualitative properties,fractional integral inequalities have also developed rapidly.In this paper,we study the existence and uniqueness of solutions of fractional differential equations by using Banach contraction mapping principle and fixed point theorem.We establish Hermite Hadamard inequality and inverse Minkowski inequality by using fractional integral operator and Holder-Iscan integral inequality.In this paper,the existence and uniqueness of fractional solutions are studied by using Banach contraction mapping principle and fixed point theorem.Hermite Hadamard inequality and inverse Minkowski inequality are established by using fractional integral operator and Holder-Iscan integral inequality.According to the content,this paper is divided into the following four chapters:Chapter 1 In the introduction,we mainly introduce the definitions and lemmas of qualitative properties of solutions of fractional differential equations.Chapter 2 In this chapter,we study the existence and uniqueness of solutions for the following fractional differential systems by using Banach contraction mapping principle,fixed point theorem and weighted norm:Chapter 3 In this chapter,we establish some inverse Minkowski inequalities and Hermite-Hadamard inequalities by using fractional integral operators and Mittag-Leffler functions,which generalize the inequalities in Kottakkaran Souppy Nisar.Chapter 4 In this chapter,by using Holder-Iscan integral inequality,Hermite-Hadamard integral inequality of integer order for s-convex function is extended to fractional integral inequality,which makes the new integral inequality have a wider research field.