Solvability Of Some Conformable Fractional Boundary Value Problems Under Barrier Strip Conditions

The conformable fractional derivative is a new definition proposed in 2014.While people have done some work on it,s properties,there’s a lot of research that’s not perfect,and there’s a lot of fundamental issues that we need to study.In this thesis,solvability of some conformable fractional boundary value proble-ms under barrier strip conditions is considered.According to the content,the structure of this thesis is as follows:In chapter one,briefly introduce the research background and status of boundary value problems of conformable fractional differential equation.In chapter two,we introduces the concepts and properties of conformable fractional differential equations and some methods used in this article.In chapter three,firstly,the definition and theorems of topology transversal theorem are given.In this paper,the existence of the solution of the two-point fractional derivative boundary value problem is studied,and the proof process is mainly based on the homotopy operator and the topology transversal theorem.Two examples are given to illustrate the results.In chapter four,the existence of solutions of three-point boundary value problems with conformable fractional derivative is studied.The research methods are mainly based on Leray-Schauder nonlinear alternative theorem and Arzela-Ascoli theorem.In chapter five,we give the existence theorem of the conformable fractional derivative of m-point boundary value problem.The methods are Leray-Schauder nonlinear alternative theorem and Arzela-Ascoli theorem.In chapter six,the summary and prospect of this thesis.