Existence And Construction Of Solutions For Terminal Value Problems Of Differential Equations

In this paper,the existence and uniqueness of terminal value problems of two kinds of differential equations are studied by means of nonlinear functional analysis: ordinary differential equation and generalized Caputo fractional differential equation.Firstly,the two differential equations are transformed into integral equations under the corresponding conditions under finite terminal values,and then the existence and uniqueness of the solutions of the integral equations are obtained by applying the fixed point theory.Finally,the applicability of the obtained results is verified by an example.The first chapter mainly introduces the background,development and research status of the terminal value problem,as well as the main work and innovation points of this paper.In Chapter 2,we discuss the existence and uniqueness of the final value problems of first order differential equations.After transforming the final value problem of the first order differential equation into an equivalent integral equation,the comparison lemma is established,and the existence and uniqueness of the solution of the integral equation is proved by using iteration technique and fixed point method.Some sufficient conditions for the existence and uniqueness of the solution of the final value problem of the first order differential equation are given.In Chapter 3,we discuss the existence of final value problems of generalized Caputo fractional differential equations.After transforming the final value problem of fractional differential equation into an equivalent integral equation,the integral operator is defined and the existence of the fixed point of the integral operator is proved by using the fixed point theorem of Schauder,and a sufficient condition for the existence of the solution of the final value problem is given.