Research On The Uniqueness Of Solutions For Nonlinear Fractional Differential Equations With Integral Boundary Value Problem

This paper mainly studies the existence and uniqueness of solutions of fractional d-ifferential equations with integral boundary value conditions,and gives the corresponding iterative sequence convergence to the unique solution.The fractional differential equation is first converted into an equivalent fractional integral equation,and in the appropriate Banach space,using the fixed point theorem of ?-(h,r)-concave operator and the related theory of mixed monotone operator,the existence and uniqueness of the studied problem are proved.This thesis is mainly divided into five chapters:Chapter 1 is the introduction,which briefly introduces the research background of the subjectIn chapter 2,we study the integral boundary value problem of fractional differential equations with parameters:???where 2<??,0<?<?,?>0 is a parameter,?:[0,1]×[0,?)?[0,?)is a continuous function.By using a lemma of concave operator,the existence and uniqueness of the positive solution of the problem are studied,and the relation between the positive solution and the parameter is also investigated.In chapter 3,the following nonlinear fractional differential equations with integral boundary value conditions are considered:???here 2<??3,0<?<?,?,p are two real numbers,??R is a parameter,J=[0,1],f:J×K?K and g:J?K are continuous.Using the fixed point theorem of ?-(h,r)-concave operator in semi-ordered set Ph,r,the existence and uniqueness of its solution are obtained.In chapter 4,we discuss the following extended fractional differential equations with integral boundary conditions:???where A is a function of bounded variation,(?)de-note the Riemann-Stieltjes integral with respect to A and are nonnegative,g(t)is continuous in[0,1].In the discussion,the degree of the higher derivative of the nonlinear item.f is different from that of the boundary conditions.By using the fixed point theorem of ?-(h,r)-concave operator defined on the ordered set,the existence and uniqueness of its solution in a special set are obtained,and an iterative form is constructed to approximate the unique solution for any initial value.In chapter 5,we use fixed point theorems in partially ordered metric spaces to consider the existence and uniqueness of solutions of the following integral boundary value problem:???...