Existence Of Solutions For Boundary Value Problems Of Several Types Of Fractional Differential Equations With P-Laplacian Operator

In recent decades,differential equations have developed rapidly and are widely used in physics,chemistry,biology and many other fields.In the process of this development,mathematicians have found that compared with integer-order differential equations,fractional differential equation models can more accurately describe natural phenomena and explain the development laws of things more accurately.As a result,fractional differential equations have received more and more attention.As an important topic in the field of differential equations,the boundary value problem has also achieved a lot of results.However,compared with the huge differential equation system,the study of it is only a drop in the ocean,and it still has great research value.Therefore,this thesis mainly study the existence of solutions of three types of fractional differential equations with p-Laplacian operator.The full text consists of five chapters:In Chapter 1,we mainly introduce the research background and development status of fractional differential equations and p-Laplacian operator.We briefly describe the main work of this thesis,and the relevant definitions and fixed point theorems required for this thesis are given.In Chapter 2,we study the boundary value problems of conformable fractional differential equation by using the Leray-Schauder nonlinear alternative and Krasnosel’skiis fixed point theorem,and the existence of solutions for this boundary value problem are obtained.Finally,give some numerical examples to prove the feasibility of the conclusion.In Chapter 3,the existence and multiplicity of the positive solutions for boundary value problems of fractional differential equation with p-Laplacian operator are given by using GuoKrasnosel’skii fixed point theorem,Leggett-Williams fixed point theorem and monotonic iteration technique,and give examples to verify.In Chapter 4,we study a class of semilinear fractional impulsive differential equation boundary value problems with p-Laplacian operator.The existence of solutions are obtained by using Schauder fixed point theorem and Schaefer fixed point theorem,and the uniqueness of solution is obtained by the Banach compression mapping principle.Finally,examples are given to verify the reasonableness of the obtained results.In Chapter 5,summarizes and prospects.We give a summary of the thesis and prospect for future research.