Existence Of Solutions To Boundary Value Problems Of Uniform Fractional Differential Equations

Boundary value problem is a common problem in fractional differential equations.There is a wide range of research on this problem like integral boundary value problem,multi-point boundary value problem and so on.The research on standard Riemann-Liouville derivatives of fractional differential equations has been deep in recent years.As a new definition,con-formable fractional derivative gradually integrated into the fractional differential equation,waiting for more and more people to explore and research.Under this background,we mainly focus on the existence of positive solutions of a class of conformable fractional order differential equation with boundary value conditions,which proves the existence of positive solutions and the related conclusions.This thesis is divided into three parts.Chapter one is the introduction,which mainly introduces the research background,research significance,its own novelty and the theoreti-cal basis of this paper,and it also introduces the necessary basic definitions,theorems and related properties of the following research.The second chapter discusses the existence of positive solution of the left conformable fractional differential equations:#12 where ? belongs to(1,2],T?? denotes the conformable fractional derivative of order ?,the function f:(a,b)×[0,?)(?)[0,?)is continuous,and 0?a<b?1.This chapter is divided into two parts,the first part studies the singularity of the function f at the point t=a,t=b,using the properties of Green's function and the fixed-point theorem on the cone,sufficient conditions are established to prove the existence and multiple positive so-lutions of the positive solutions of the left consistent fractional differential equations.The second part studies the existence of positive solutions in the case of continuous functions.Finally,a simple example is given to illustrate it.The third chapter discusses the existence of conformable fractional differential equations with integral boundary value problems:#12 where a belongs to(1,2],T? denotes the conformable fractional derivative of order ?,the function f:[0,1]×[0,?)(?)[0,?)is continuous,and L(x)=??0 1 x(t)dt for which the parameter ? is a positive number.Our research based on the method of upper and lower solutions,we give some existence and unique results by using and Schauder fixed point theorem.