Positive Solutions For Three Kinds Of Boundary Value Problems With Conformable Fractional Derivatives

In this paper, by using the fixed-point theory on cone, the existence and multiplicity of positive solutions of boundary value problems with conformable fractional derivative are considered and gives the corresponding Laplace transform. According to the content, the full text is divided into six chapters:In chapter one, we introduce the research background and development of boundary value problems of differential equations.The chapter second introduces the related definitions of fractional differential equations and lemmas. Through the calculation, we give the Green function of fractional differential equation boundary value problem with conformable fractional derivative. Give the Laplace transformation of linear homogeneous problem. And the two important theorems - uniform convergence theorem of the function family and fixed point theorem be proposed.In chapter three, we study the positive solutions of nonlinear boundary value problems with conformable fractional derivatives. Firstly, give the integral operator of the problem and prove its completely continuous. And then we give the results, i.e. control the nonlinear term, use the cone fixed point theorem proving the existence and multiplicity of positive solutions of the problem. Finally Laplace transformation is given.In chapter four, on the basis of the previous chapter, we study the nonlinear eigenvalue problem with conformable fractional derivative. The existence of positive solutions is got by eigenvalue criterion is given, that process also used the fixed point theorem.In chapter five, we research the positive solutions to boundary value problems of P-Laplacian with conformable fractional derivatives. The integral operator corresponding to the boundary value problem is given. By using the properties of the Laplace operator, we obtain the complete continuity of the integral operator, and then prove the existence and multiplicity of positive solutions of the problem by using the fixed point theorem.The sixth chapter is the summary and prospect of this paper.