Existence Of Solutions To Several Classes Of Nonlinear Fractional Differential Equations

With the development of science and technology and the progress of the times,frac?tional order equation theory has been gradually improved.In recent years,fractional order differential equations have been widely used in many fields such as aerodynamics,control engineering and biophysics.In this paper,some boundary value problems of fractional differ-ential equations are discussed,and the existence of the solutions and their related conclusions are obtained.It is divided into the following four parts.The first chapter is the introduction,in which we mainly give the definition and lemma needed in the process of solving fractional differential equation.In the second chapter,we study a class of conformable fractional differential equation systems with coupled integral boundary conditions(?) By using the Krasnosel'skii fixed point theorem,the existence of positive solutions is proved.In chapter three,we discuss a class of nonlinear singular semipositone fractional differ-ential problems with integral boundary conditions(?) The existence of positive solutions is proved by employing the fixed point theorem on cone and Leray-Schauder alternative theory.The fourth chapter is to deals with the existence of positive solutions for the following singular nonlinear fractional differential problems with multi-point boundary conditions(?) As application of the properties of the first eigenvalue corresponding to relevant operator and some new height functions,the existence and multiplicity of positive solutions are proved by virtue of the fixed point index theorem.