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

The main content of this thesis is the solution of fractional differential equations with p-Laplacian operator and p(t)-Laplacian operator under different boundary value conditions,and the singularity and semi-positone of nonlinear terms will be discussed.In this thesis,the differential equation is transformed into an equivalent integral equation by using the boundary value condition,and then the Schaefer fixed point theorem,Kransnosel’skii fixed point theorem and the Banach compressed image principle are used to verify the existence and uniqueness of the solution about the studied equations.This thesis consists of six chapters.The first chapter is introduction,which mainly describes the historical background of the research problems,the significance of the topic selection and the current research status,as well as some related definitions,lemmas and theorems.In chapter 2,the solution of fractional differential equations with p-Laplacian operator under anti-periodic boundary value problem will be studied,and the singularity of nonlinear terms is discussed.And then,Kransnosel’skii fixed point theorem and the principle of Banach compressed image are used to verify the existence and uniqueness of the solution about the studied equation.In chapter 3,the solution of the fractional impulsive differential equation with p-Laplacian operator under the condition of the nonlinear terms with singularity will be studied.And then,Schaefer fixed point theorem and the principle of Banach compressed image are used to verify the existence and uniqueness of the solution of the studied equation.In chapter 4,the solution of fractional impulsive differential equations with the p(t)-Laplacian operator under the condition of generalized anti-periodic boundary value will be studied,where the p(t)-Laplacian operator is the generalization of p-Laplacian.And then,Kransnosel’skii fixed point theorem and the principle of Banach compressed image are used to verify the existence and uniqueness of the solution about the studied equation.In chapter 5,we study fractional differential equations with p(t)-Laplacian operator,anti-perciodic boundary value problem with impulse term and nonlinear term with positive semi-positive.And then,Schaefer fixed point theorem and Banach compressed image principle are used to verify the existence and uniqueness of the solution about the studied equation.In chapter 6,Summary and Outlook.The chapter mainly summarize the research questions and point out the shortcomings of this thesis,as well as putting forward the further research directions and ideas for follow-up on such problems.