Existence Of Solutions To Boundary Value Problems Of Two Types Of Fractional Differential Equations

In recent years,with the rapid development of science and technology,the application domain of fractional differential equation is gradually expanded.In addition to mathematics,it is also widely used in the field of biological,chemistry and physics.Therefore,the study for the existence and uniqueness of solutions to fractional differential equations has its important practical application value,in addition to its own theoretical significance.In this paper,we mainly study two kinds of problems about the exis-tence of solutions to fractional differential equations.The thesis is divid-ed into three chapters.The chapter 1,we mainly introduces some the-orems about fractional differential equations and some definitions that we will need in this thesis.The chapter 2,we consider a kind of m-point fractional boundary value problem on an infinite intervalOn the basis of[3][4][5],this chapter extend the condition of the boundary value problem to an infinite interval.And we use three meth-ods to get the existence of solutions.Firstly,under the condition of H1,H2,H3,we use a kind of fixed point theorem to get multiple pos-itive solutions.Secondly,by using L-set contraction mapping principle and contracting mapping principle,we get the existence and uniqueness of the solution.Lastly,under the condition of H12,we can get the ex-istence and uniqueness of the positive solution of the equation by using the contracting mapping principle.In chapter 3,we consider a kind of fractional differential equation nonlocal boundary value problemOn the basis of[18][19],we can get the only positive solution by using a kind of concave operator fixed point theorem and its deduction under the condition of H13,H14,H15.