Existence And Uniqueness Of Solutions For Boundary Value Problems Of Fractional Impulsive Differential Equations With P-Laplacian Operators

In this paper,we discuss the existence and uniqueness of the solution of Fractional differential equation boundary value problem with p-Laplacian operator,impulse term and nonlinear term.This paper consists of three parts:introduction,discussion and demonstration of boundary value problem,summary and prospect.The specific content is as follows:The introduction part is the background of this paper.The discussion and demonstration of boundary value problem are chapters 2,3 and 4.The first chapter gives the relevant knowledge and preliminary lemma of fractional calculus required in this paper.In chapter 2,we discuss the uniqueness of positive solutions for a class of singular fractional boundary value problems with p-Laplacian operator when 2<??3.According to the conditions,the corresponding Green function of the problem is obtained.Then,by using the fixed point theorem for partial ordered sets,the sufficient conditions for the uniqueness of positive solutions of singular boundary value problems with p-Laplacian operators are obtained.In the next two chapters,we consider the solutions of several classes of boundary value problems for fractional impulsive differential equations with p-Laplacian operators whose derivatives are Caputo fractional derivatives.Where the p-Laplacian operator is defined as:?p(s)=|s|p-2s,p>1,(?q)-1(s)=?p(s),1/p+1/q=1.In chapter 3,the boundary value problem of fractional p-Laplacian impulse differential equations is studied for 2<?<3.Firstly,according to the known conditions,the impulse problem is transformed into an equivalent integral equation.Finally,the sufficient conditions for the existence and uniqueness of solutions are given by using Leray-Schauder fixed point theorem and Banach compression image principle.The results are verified by an example.In chapter 4,the research of p-Laplacian operator fractional order impulsive differential equation with singular boundary value problems of existence and uniqueness of solution.First of all,the corresponding Green function is deduced,and get some properties of the Green function,then using cone compression stretching cone fixed point theorem and the existing results of singular problem is deduced on the Fractional order with p-Laplacian operator of impulsive differential equation with singular existence and uniqueness theorem of solutions of boundary value problems.Chapter 5 summarizes the above problems.By studying such problems,sufficient conditions for the existence and uniqueness of solutions of such boundary value problems under different conditions are obtained,and the deficiencies and improvements of this research are proposed.