Research On The Existence And Uniqueness Of Positive Solutions Of Two Types Of Fractional Differential Equations

This paper mainly studies the existence and uniqueness of positive solutions of two types of fractional differential equations.The article is divided into two parts to explain.The first part uses the fixed point theorem of the mixed monotone operator equation to study the existence and uniqueness of the positive solution of a class of nonlinear fractional differential equations with derivative terms and three-point boundary conditions;Partially use the new fixed point theorem to study the existence and uniqueness of positive solutions of a class of coupled fractional differential equations with multi-point boundary value conditions.The details are as follows:In the second chapter,we introduces the first problem of this paper.Using the fixed point theorem of mixed monotone operator equations,combining Green's function and fixed point theorem on cones,the existence and uniqueness of the positive solution of the equation is obtained,and two iterations are constructed.Sequence to approximate the solution.The difficulty of the fractional differential equation after adding the derivative term lies in the calculation of the fractional Green's function and the determination of its range,as well as the definition of the set norm and the semi-ordered relationship it is given.This difficulty is overcome by the nature of Green's function.In the third chapter,we studies a class of coupled fractional differential equations with multipoint boundary value conditions.Use the new fixed point theorem to analyze the existence and uniqueness of the positive solution of this equation.The solution of the problem is obtained by using the properties of Green's function,and the existence and uniqueness of the solution of the equation are proved.