Fractional Order Differential Equations With Boundary Value Problems And Existence Of Solutions For Differential Inclusions

In this master's thesis,with the definition of the conformable fractional derivative,we study the existence of solution of nonlinear conformable differential equations with functional boundary conditions and differential inclusions with general nonlinear boundary conditions.The main methods include solution-tube,upper and lower solutions,comparison principles,Schauder's fixed-point theorem and a fixed point theorem for condensing map.The article is including the following five parts:Chapter one is the introduction,we review the research background of fractional differential equations or differential inclusions and the overall layout of the article.Chapter two is the prearrangement knowledge,we introduce the definitions,properties,calculation and related theorems of the conformable fractional derivative,and the solutions of the related linear equations and the formulas of their Green functions are also showed.In the third chapter,we study the existence of solution of the nonlinear conformable differential equations,here we consider the functional boundary condition,where the right member of the system is L?1-Caratheodory function.Several examples are listed to show the validity of the results.In the forth chapter,we utilize a fixed point theorem for condensing maps combined with upper and lower solutions,then obtain the existence of solutions for differential inclusions with nonlinear boundary condition.The last chapter is the summary and prospect of this thesis.